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Journal articles on the topic 'Automated Theorem Prover'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Ophelders, W. M. J., and H. C. M. De Swart. "Tableaux Versus Resolution a Comparison." Fundamenta Informaticae 18, no. 2-4 (1993): 109–27. http://dx.doi.org/10.3233/fi-1993-182-403.

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In [13] we have presented the ideas underlying an automated theorem prover based on tableaux extended with unification under restrictions. In [6] a full description of an implementation of this theorem prover in PROLOG is given. In this paper we first shortly repeat the main ideas, referring to [13] for more details. Next we present the test results of our theorem prover mainly with respect to Pelletier’s 75 problems for testing automatic theorem provers ([7]). We also give a comparison of our results with the results obtained by the resolution-based theorem provers PCPROVE and OTTER and by th

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Crouse, Maxwell, Ibrahim Abdelaziz, Bassem Makni, et al. "A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 7 (2021): 6279–87. http://dx.doi.org/10.1609/aaai.v35i7.16780.

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Automated theorem provers have traditionally relied on manually tuned heuristics to guide how they perform proof search. Deep reinforcement learning has been proposed as a way to obviate the need for such heuristics, however, its deployment in automated theorem proving remains a challenge. In this paper we introduce TRAIL, a system that applies deep reinforcement learning to saturation-based theorem proving. TRAIL leverages (a) a novel neural representation of the state of a theorem prover and (b) a novel characterization of the inference selection process in terms of an attention-based action

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WANG, Zhen-Ming, Yi-Yun CHEN, and Zhi-Fang WANG. "Automated Theorem Prover for Pointer Logic." Journal of Software 20, no. 8 (2009): 2037–50. http://dx.doi.org/10.3724/sp.j.1001.2009.00572.

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Vor der Brück, Tim, and Hermann Helbig. "Meronymy Extraction Using An Automated Theorem Prover." Journal for Language Technology and Computational Linguistics 25, no. 1 (2010): 57–81. http://dx.doi.org/10.21248/jlcl.25.2010.129.

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WOLF, ANDREAS, and REINHOLD LETZ. "STRATEGY PARALLELISM IN AUTOMATED THEOREM PROVING." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 02 (1999): 219–45. http://dx.doi.org/10.1142/s0218001499000136.

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Automated theorem provers use search strategies. Unfortunately, there is no unique strategy which is uniformly successful on all problems. This motivates us to apply different strategies in parallel, in a competitive manner. In this paper, we discuss properties, problems, and perspectives of strategy parallelism in theorem proving. We develop basic concepts like the complementarity and the overlap value of strategy sets. Some of the problems such as initial strategy selection and run-time strategy exchange are discussed in more detail. The paper also contains the description of an implementati

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Jan, Jakubuv, and Kaliszyk Cezary. "Relaxed Weighted Path Order in Theorem Proving." Mathematics in Computer Science 14, no. 3 (2020): 657——670. https://doi.org/10.1007/s11786-020-00474-0.

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We propose an extension of the automated theorem prover E by the weighted path order- ing (WPO). Weighted path ordering is theoretically stronger than all the orderings used in E Prover, however its parametrization is more involved than those normally used in automated reasoning. In particular, it depends on a term algebra. We integrate the ordering in E Prover and perform an eval- uation on the standard theorem proving benchmarks. The ordering is complementary to the ones used in E prover so far. Furthermore, first-time presented here, we propose a relaxed variant of the weighted path order a

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Elnadi, Tarek Mohamed, and Albert Hoogewijs. "KARNAK {$\star$}: an automated theorem prover for PPC {$\star$}." Bulletin of the Belgian Mathematical Society - Simon Stevin 2, no. 5 (1995): 541–71. http://dx.doi.org/10.36045/bbms/1103408677.

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KANSO, KARIM, and ANTON SETZER. "A light-weight integration of automated and interactive theorem proving." Mathematical Structures in Computer Science 26, no. 1 (2014): 129–53. http://dx.doi.org/10.1017/s0960129514000140.

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In this paper, aimed at dependently typed programmers, we present a novel connection between automated and interactive theorem proving paradigms. The novelty is that the connection offers a better trade-off between usability, efficiency and soundness when compared to existing techniques. This technique allows for a powerful interactive proof framework that facilitates efficient verification of finite domain theorems and guided construction of the proof of infinite domain theorems. Such situations typically occur with industrial verification. As a case study, an embedding of SAT and CTL model c

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Cao, Feng, Yang Xu, Jun Liu, Shuwei Chen, and Xinran Ning. "CSE_E 1.0: An Integrated Automated Theorem Prover for First-Order Logic." Symmetry 11, no. 9 (2019): 1142. http://dx.doi.org/10.3390/sym11091142.

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First-order logic is an important part of mathematical logic, and automated theorem proving is an interdisciplinary field of mathematics and computer science. The paper presents an automated theorem prover for first-order logic, called C S E _ E 1.0, which is a combination of two provers contradiction separation extension (CSE) and E, where CSE is based on the recently-introduced multi-clause standard contradiction separation (S-CS) calculus for first-order logic and E is the well-known equational theorem prover for first-order logic based on superposition and rewriting. The motivation of the

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Baghdasaryan, Ashot, and Hovhannes Bolibekyan. "On Recurrent Neural Network Based Theorem Prover For First Order Minimal Logic." JUCS - Journal of Universal Computer Science 27, no. (11) (2021): 1193–202. https://doi.org/10.3897/jucs.76563.

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There are three main problems for theorem proving with a standard cut-free system for the first order minimal logic. The first problem is the possibility of looping. Secondly, it might generate proofs which are permutations of each other. Finally, during the proof some choice should be made to decide which rules to apply and where to use them. New systems with history mechanisms were introduced for solving the looping problems of automated theorem provers in the first order minimal logic. In order to solve the rule selection problem, recurrent neural networks are deployed and they are used to

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Guo, Dakai, and Wensheng Yu. "A Comprehensive Formalization of Propositional Logic in Coq: Deduction Systems, Meta-Theorems, and Automation Tactics." Mathematics 11, no. 11 (2023): 2504. http://dx.doi.org/10.3390/math11112504.

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The increasing significance of theorem proving-based formalization in mathematics and computer science highlights the necessity for formalizing foundational mathematical theories. In this work, we employ the Coq interactive theorem prover to methodically formalize the language, semantics, and syntax of propositional logic, a fundamental aspect of mathematical reasoning and proof construction. We construct four Hilbert-style axiom systems and a natural deduction system for propositional logic, and establish their equivalences through meticulous proofs. Moreover, we provide formal proofs for ess

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Schon, Claudia, Sophie Siebert, and Frieder Stolzenburg. "Using ConceptNet to Teach Common Sense to an Automated Theorem Prover." Electronic Proceedings in Theoretical Computer Science 311 (December 31, 2019): 19–24. http://dx.doi.org/10.4204/eptcs.311.3.

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13

Santos, Vanda, Joana Teles, and Pedro Quaresma. "Exploring Quadrilaterals: An Interactive Task for 7th Grade Students Using GeoGebra Classroom." International Journal for Technology in Mathematics Education 31, no. 3 (2024): 107–16. http://dx.doi.org/10.1564/tme_v31.3.01.

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Using a Dynamic Geometry System (DGS) students can engage in a dynamic learning process that allows them to experiment, create strategies, make conjectures, argue, and deduce mathematical properties. A DGS enables the introduction of proofs, by providing visual aids. The proof of the conjectures made emerges as the next step towards formalising and understanding the contents covered and the introduction of automated deduction systems at schools can be an added value. The implementation of automated deduction systems in schools faces several challenges, such as curriculum-issues, teacher knowle

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Baghdasaryan, Ashot, and Hovhannes Bolibekyan. "On Recurrent Neural Network Based Theorem Prover For First Order Minimal Logic." JUCS - Journal of Universal Computer Science 27, no. 11 (2021): 1193–202. http://dx.doi.org/10.3897/jucs.76563.

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There are three main problems for theorem proving with a standard cut-free system for the first order minimal logic. The first problem is the possibility of looping. Secondly, it might generate proofs which are permutations of each other. Finally, during the proof some choice should be made to decide which rules to apply and where to use them. New systems with history mechanisms were introduced for solving the looping problems of automated theorem provers in the first order minimal logic. In order to solve the rule selection problem, recurrent neural networks are deployed and they are used to

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IBENS, ORTRUN, and MARC FUCHS. "AN AUTOMATED THEOREM PROVER BASED ON CONNECTION TABLEAU CALCULI WITH DISJUNCTIVE CONSTRAINTS." International Journal on Artificial Intelligence Tools 10, no. 01n02 (2001): 181–98. http://dx.doi.org/10.1142/s0218213001000477.

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Automated theorem proving with connection tableau calculi imposes search problems in tremendous search spaces. In this paper, we present a new approach to search space reduction in connection tableau calculi. In our approach structurally similar parts of the search space are compressed by means of disjunctive constraints. We describe the necessary changes of the calculus, and we develop elaborate techniques for an efficient constraint processing. Moreover, we present an experimental evaluation of our approach.

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HOMMERSOM, ARJEN, PETER J. F. LUCAS, and PATRICK VAN BOMMEL. "Checking the quality of clinical guidelines using automated reasoning tools." Theory and Practice of Logic Programming 8, no. 5-6 (2008): 611–41. http://dx.doi.org/10.1017/s1471068408003451.

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AbstractRequirements about the quality of clinical guidelines can be represented by schemata borrowed from the theory of abductive diagnosis, using temporal logic to model the time-oriented aspects expressed in a guideline. Previously, we have shown that these requirements can be verified using interactive theorem proving techniques. In this paper, we investigate how this approach can be mapped to the facilities of a resolution-based theorem prover,otterand a complementary program that searches for finite models of first-order statements,mace-2. It is shown that the reasoning required for chec

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DENNEY, EWEN, BERND FISCHER, and JOHANN SCHUMANN. "AN EMPIRICAL EVALUATION OF AUTOMATED THEOREM PROVERS IN SOFTWARE CERTIFICATION." International Journal on Artificial Intelligence Tools 15, no. 01 (2006): 81–107. http://dx.doi.org/10.1142/s0218213006002576.

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We describe a system for the automated certification of safety properties of NASA software. The system uses Hoare-style program verification technology to generate proof obligations which are then processed by an automated first-order theorem prover (ATP). We discuss the unique requirements this application places on the ATPs, focusing on automation, proof checking, traceability, and usability, and describe the resulting system architecture, including a certification browser that maintains and displays links between obligations and source code locations. For full automation, the obligations mu

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18

Steen, Alexander. "Higher-order theorem proving and its applications." it - Information Technology 61, no. 4 (2019): 187–91. http://dx.doi.org/10.1515/itit-2019-0001.

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Abstract Automated theorem proving systems validate or refute whether a conjecture is a logical consequence of a given set of assumptions. Higher-order provers have been successfully applied in academic and industrial applications, such as planning, software and hardware verification, or knowledge-based systems. Recent studies moreover suggest that automation of higher-order logic, in particular, yields effective means for reasoning within expressive non-classical logics, enabling a whole new range of applications, including computer-assisted formal analysis of arguments in metaphysics. My wor

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Vujosevic-Janicic, Milena, Filip Maric, and Dusan Tosic. "Using simplex method in verifying software safety." Yugoslav Journal of Operations Research 19, no. 1 (2009): 133–48. http://dx.doi.org/10.2298/yjor0901133v.

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In this paper we have discussed the application of the Simplex method in checking software safety - the application in automated detection of buffer overflows in C programs. This problem is important because buffer overflows are suitable targets for hackers' security attacks and sources of serious program misbehavior. We have also described our implementation, including a system for generating software correctness conditions and a Simplex based theorem prover that resolves these conditions.

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Trinh, Trieu H., Yuhuai Wu, Quoc V. Le, He He, and Thang Luong. "Solving olympiad geometry without human demonstrations." Nature 625, no. 7995 (2024): 476–82. http://dx.doi.org/10.1038/s41586-023-06747-5.

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AbstractProving mathematical theorems at the olympiad level represents a notable milestone in human-level automated reasoning1–4, owing to their reputed difficulty among the world’s best talents in pre-university mathematics. Current machine-learning approaches, however, are not applicable to most mathematical domains owing to the high cost of translating human proofs into machine-verifiable format. The problem is even worse for geometry because of its unique translation challenges1,5, resulting in severe scarcity of training data. We propose AlphaGeometry, a theorem prover for Euclidean plane

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MYREEN, MAGNUS O., and SCOTT OWENS. "Proof-producing translation of higher-order logic into pure and stateful ML." Journal of Functional Programming 24, no. 2-3 (2014): 284–315. http://dx.doi.org/10.1017/s0956796813000282.

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AbstractThe higher-order logic found in proof assistants such as Coq and various HOL systems provides a convenient setting for the development and verification of functional programs. However, to efficiently run these programs, they must be converted (or ‘extracted’) to functional programs in a programming language such as ML or Haskell. With current techniques, this step, which must be trusted, relates similar looking objects that have very different semantic definitions, such as the set-theoretic model of a logic and the operational semantics of a programming language. In this paper, we show

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Lee, Scott, Gillian Dobbie, Jing Sun, and Lindsay Groves. "Formal Verification of Semistructured Data Models in PVS." JUCS - Journal of Universal Computer Science 15, no. (1) (2009): 241–72. https://doi.org/10.3217/jucs-015-01-0241.

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The rapid growth of the World Wide Web has resulted in a dramatic increase in semistructured data usage, creating a growing need for effective and efficient utilization of semistructured data. In order to verify the correctness of semistructured data design, precise descriptions of the schemas and transformations on the schemas must be established. One effective way to achieve this goal is through formal modeling and automated verification. This paper presents the first step towards this goal. In our approach, we have formally specified the semantics of the ORA-SS (Object-Relationship-Attribut

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Kalla, Hamoudi, David Berner, and Jean-Pierre Talpin. "Automated Generation of Synchronous Formal Models from SystemC Descriptions." Journal of Circuits, Systems and Computers 28, no. 04 (2019): 1950061. http://dx.doi.org/10.1142/s0218126619500610.

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SystemC is one of the most popular electronic system-level design language and it is embraced by a growing community that seeks to move to a higher level of abstraction. It lacks however a standard way of integrating formal methods and formal verification techniques into a SystemC design flow. In this paper, we show how SystemC descriptions are automatically transformed into the formal synchronous language Signal, while conserving the original structure and enabling the application of formal verification techniques. Signal provides a simple semantics of concurrency and time, and allows verific

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Zakhour, George, Pascal Weisenburger, Jahrim Gabriele Cesario, and Guido Salvaneschi. "Dis/Equality Graphs." Proceedings of the ACM on Programming Languages 9, POPL (2025): 2282–305. https://doi.org/10.1145/3704913.

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E-graphs are a data structure to compactly represent a program space and reason about equality of program terms. E-graphs have been successfully applied to a number of domains, including program optimization and automated theorem proving. In many applications, however, it is necessary to reason about disequality of terms as well as equality. While disequality reasoning can be encoded, direct support for disequalities increases performance and simplifies the metatheory. In this paper, we develop a framework independent of a specific implementation to formally reason about e-graphs. For the firs

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Stjerna, Amanda, and Philipp Rümmer. "A Constraint Solving Approach to Parikh Images of Regular Languages." Proceedings of the ACM on Programming Languages 8, OOPSLA1 (2024): 1235–63. http://dx.doi.org/10.1145/3649855.

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A common problem in string constraint solvers is computing the Parikh image, a linear arithmetic formula that describes all possible combinations of character counts in strings of a given language. Automata-based string solvers frequently need to compute the Parikh image of products (or intersections) of finite-state automata, in particular when solving string constraints that also include the integer data-type due to operations like string length and indexing. In this context, the computation of Parikh images often turns out to be both prohibitively slow and memory-intensive. This paper contr

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PAGE, REX. "Engineering Software Correctness." Journal of Functional Programming 17, no. 6 (2007): 675–86. http://dx.doi.org/10.1017/s095679680700634x.

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AbstractDesign and quality are fundamental themes in engineering education. Functional programming builds software from small components, a central element of good design, and facilitates reasoning about correctness, an important aspect of quality. Software engineering courses that employ functional programming provide a platform for educating students in the design of quality software. This pearl describes experiments in the use of ACL2, a purely functional subset of Common Lisp with an embedded mechanical logic, to focus on design and correctness in software engineering courses. Students fin

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Rouached, Mohsen, Walid Fdhila, and Claude Godart. "Web Services Compositions Modelling and Choreographies Analysis." International Journal of Web Services Research 7, no. 2 (2010): 87–110. http://dx.doi.org/10.4018/jwsr.2010040105.

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In Rouached et al. (2006) and Rouached and Godart (2007) the authors described the semantics of WSBPEL by way of mapping each of the WSBPEL (Arkin et al., 2004) constructs to the EC algebra and building a model of the process behaviour. With these mapping rules, the authors describe a modelling approach of a process defined for a single Web service composition. However, this modelling is limited to a local view and can only be used to model the behaviour of a single process. The authors further the semantic mapping to include Web service composition interactions through modelling Web service c

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Davydov, Artem, Aleksandr Larionov, and Nadezhda Nagul. "Analysis and Control of Partially Observed Discrete-Event Systems via Positively Constructed Formulas." Computation 12, no. 5 (2024): 95. http://dx.doi.org/10.3390/computation12050095.

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This paper establishes a connection between control theory for partially observed discrete-event systems (DESs) and automated theorem proving (ATP) in the calculus of positively constructed formulas (PCFs). The language of PCFs is a complete first-order language providing a powerful tool for qualitative analysis of dynamical systems. Based on ATP in the PCF calculus, a new technique is suggested for checking observability as a property of formal languages, which is necessary for the existence of supervisory control of DESs. In the case of violation of observability, words causing a conflict ca

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Sivaraman, Aishwarya, Alex Sanchez-Stern, Bretton Chen, Sorin Lerner, and Todd Millstein. "Data-driven lemma synthesis for interactive proofs." Proceedings of the ACM on Programming Languages 6, OOPSLA2 (2022): 505–31. http://dx.doi.org/10.1145/3563306.

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Interactive proofs of theorems often require auxiliary helper lemmas to prove the desired theorem. Existing approaches for automatically synthesizing helper lemmas fall into two broad categories. Some approaches are goal-directed, producing lemmas specifically to help a user make progress from a given proof state, but they have limited expressiveness in terms of the lemmas that can be produced. Other approaches are highly expressive, able to generate arbitrary lemmas from a given grammar, but they are completely undirected and hence not amenable to interactive usage. In this paper, we develop

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Lam, Vitus. "Constraint-based reasoning on declarative process execution with the logics workbench." Business Process Management Journal 21, no. 3 (2015): 586–609. http://dx.doi.org/10.1108/bpmj-10-2014-0092.

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Purpose – An integral part of declarative process modelling is to guarantee that the execution of a declarative workflow is compliant with the respective business rules. The purpose of this paper is to establish a formal framework for representing business rules and determining whether any business rules are violated during the executions of declarative process models. Design/methodology/approach – In the approach, a business rule is phrased in terms of restricted English that is related to a constraint template. Linear temporal logic (LTL) is employed as a formalism for defining the set of co

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Wang, Jiawei, Cheng Li, Kai Ma, et al. "AUTOGR." Proceedings of the VLDB Endowment 14, no. 9 (2021): 1517–30. http://dx.doi.org/10.14778/3461535.3461541.

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Geo-replication is essential for providing low latency response and quality Internet services. However, designing fast and correct geo-replicated services is challenging due to the complex trade-off between performance and consistency semantics in optimizing the expensive cross-site coordination. State-of-the-art solutions rely on programmers to derive sufficient application-specific invariants and code specifications, which is both time-consuming and error-prone. In this paper, we propose an end-to-end geo-replication deployment framework AUTOGR (AUTOmated Geo-Replication) to free programmers

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GONTHIER, GEORGES, BETA ZILIANI, ALEKSANDAR NANEVSKI, and DEREK DREYER. "How to make ad hoc proof automation less ad hoc." Journal of Functional Programming 23, no. 4 (2013): 357–401. http://dx.doi.org/10.1017/s0956796813000051.

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AbstractMost interactive theorem provers provide support for some form of user-customizable proof automation. In a number of popular systems, such as Coq and Isabelle, this automation is achieved primarily through tactics, which are programmed in a separate language from that of the prover's base logic. While tactics are clearly useful in practice, they can be difficult to maintain and compose because, unlike lemmas, their behavior cannot be specified within the expressive type system of the prover itself.We propose a novel approach to proof automation in Coq that allows the user to specify th

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Sigley, Sarah, and Olaf Beyersdorff. "Proof Complexity of Modal Resolution." Journal of Automated Reasoning 66, no. 1 (2021): 1–41. http://dx.doi.org/10.1007/s10817-021-09609-9.

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AbstractWe investigate the proof complexity of modal resolution systems developed by Nalon and Dixon (J Algorithms 62(3–4):117–134, 2007) and Nalon et al. (in: Automated reasoning with analytic Tableaux and related methods—24th international conference, (TABLEAUX’15), pp 185–200, 2015), which form the basis of modal theorem proving (Nalon et al., in: Proceedings of the twenty-sixth international joint conference on artificial intelligence (IJCAI’17), pp 4919–4923, 2017). We complement these calculi by a new tighter variant and show that proofs can be efficiently translated between all these va

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Kondratyev, Dmitry A., and Alexei V. Promsky. "The Complex Approach of the C-lightVer System to the Automated Error Localization in C-programs." Modeling and Analysis of Information Systems 26, no. 4 (2019): 502–19. http://dx.doi.org/10.18255/1818-1015-2019-4-502-519.

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The C-lightVer system for the deductive verification of C programs is being developed at the IIS SB RAS. Based on the two-level architecture of the system, the C-light input language is translated into the intermediate C-kernel language. The meta generator of the correctness conditions receives the C-kernel program and Hoare logic for the C-kernel as input. To solve the well-known problem of determining loop invariants, the definite iteration approach was chosen. The body of the definite iteration loop is executed once for each element of the finite dimensional data structure, and the inferenc

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Ruo, Ando, and Takefuji Yoshiyasu. "Experiments of Randomized Hints on an Axiom of Infinite-Valued Lukasiewicz Logic." International Journal of Novel Research in Computer Science and Software Engineering 10, no. 3 (2023): 1–6. https://doi.org/10.5281/zenodo.8307890.

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<strong>Abstract:</strong> In this paper, we present an experiment of our randomized hints strategy of automated reasoning for yielding Axiom(5) from Axiom(1)(2)(3)(4) of Infinite-Valued Lukasiewicz Logic. In the experiment, we randomly generated a set of hints with size ranging from 30 to 60 for guiding hyper-resolution based search by the theorem prover. We have successfully found the most useful hints list (with 30 clauses) among 150 * 6 hints lists. Also, we discuss a curious non-linear increase of generated clauses in deducing Axiom(5) by applying our randomized hints strategy. <strong>Ke

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Xu, Wenjing, and Dianfu Ma. "A Framework for Model and Verification of Safety-Critical Operating System Based on ARINC653." Electronics 10, no. 16 (2021): 1934. http://dx.doi.org/10.3390/electronics10161934.

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As the scale and complexity of safety-critical software continue to grow, it is necessary to ensure safety and reliability to avoid minor errors leading to catastrophic disasters. Meantime, the traditional method, such as testing and simulation alone is insufficient to ensure the correctness of systems. This leads to using formal methods to provide sufficient evidence for systems. However, design a high assurance safety-critical system by formal methods is challenging due to the complexity of operating systems. In addition, the traditional interactive theorem prover used in system verification

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Kühlwein, Daniel, and Josef Urban. "MaLeS: A Framework for Automatic Tuning of Automated Theorem Provers." Journal of Automated Reasoning 55, no. 2 (2015): 91–116. http://dx.doi.org/10.1007/s10817-015-9329-1.

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Hernández-Orozco, Santiago, Francisco Hernández-Quiroz, Hector Zenil, and Wilfried Sieg. "Shortening of Proof Length is Elusive for Theorem Provers." Parallel Processing Letters 30, no. 04 (2020): 2050013. http://dx.doi.org/10.1142/s0129626420500139.

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There are many examples of failed strategies whose intention is to optimize a process but instead they produce worse results than no strategy at all. Many fall under the loose umbrella of the “no free lunch theorem”. In this paper we present an example in which a simple (but assumedly naive) strategy intended to shorten proof lengths in the propositional calculus produces results that are significantly worse than those achieved without any method to try to shorten proofs.This contrast with what was to be expected intuitively, namely no improvement in the length of the proofs. Another surprisin

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Baeta, Nuno, and Pedro Quaresma. "Towards Ranking Geometric Automated Theorem Provers." Electronic Proceedings in Theoretical Computer Science 290 (April 1, 2019): 30–37. http://dx.doi.org/10.4204/eptcs.290.3.

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Kozlov, Valery, Alexander Tatashev, and Marina Yashina. "Elementary Cellular Automata as Invariant under Conjugation Transformation or Combination of Conjugation and Reflection Transformations, and Applications to Traffic Modeling." Mathematics 10, no. 19 (2022): 3541. http://dx.doi.org/10.3390/math10193541.

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This paper develops the analysis of properties of the cellular automata class introduced by the authors. It is assumed that the set of automaton cells is finite and forms a closed lattice, and there are two states for each automaton cell. We consider a new concept. This concept is the average velocity of a cellular automaton, which characterizes the average intensity of changes in the states of the automaton’s cells for a given initial state. The automaton velocity is equal to 1 if the state of any cell changes at each step. The spectrum of average velocities of a cellular automaton is the set

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BURGIN, MARK. "DECIDABILITY AND UNIVERSALITY IN THE AXIOMATIC THEORY OF COMPUTABILITY AND ALGORITHMS." International Journal of Foundations of Computer Science 23, no. 07 (2012): 1465–80. http://dx.doi.org/10.1142/s012905411240059x.

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In this paper, we study to what extent decidability is connected to universality. A natural context for such a study is provided by the axiomatic theory of computability, automata and algorithms. In Section 2, we introduce necessary concepts, constructions, axioms, postulates, conditions and problems. Section 3 contains the main results of the paper. In particular, it is demonstrated (Theorems 1 and 2) that undecidability of algorithmic problems does not depend on existence of universal algorithms and may be caused by weaker conditions. At the same time, results of Theorems 2 and 3 demonstrate

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Paul, Satyam, Rob Turnbull, Davood Khodadad, and Magnus Löfstrand. "A Vibration Based Automatic Fault Detection Scheme for Drilling Process Using Type-2 Fuzzy Logic." Algorithms 15, no. 8 (2022): 284. http://dx.doi.org/10.3390/a15080284.

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The fault detection system using automated concepts is a crucial aspect of the industrial process. The automated system can contribute efficiently in minimizing equipment downtime therefore improving the production process cost. This paper highlights a novel model based fault detection (FD) approach combined with an interval type-2 (IT2) Takagi–Sugeno (T–S) fuzzy system for fault detection in the drilling process. The system uncertainty is considered prevailing during the process, and type-2 fuzzy methodology is utilized to deal with these uncertainties in an effective way. Two theorems are de

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Ganesalingam, M., and W. T. Gowers. "A Fully Automatic Theorem Prover with Human-Style Output." Journal of Automated Reasoning 58, no. 2 (2016): 253–91. http://dx.doi.org/10.1007/s10817-016-9377-1.

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Dordopulo, A. I. "APPLICATION OF PERFORMANCE REDUCTION METHODS FOR MINIMIZATION OF ANALYZED NUMBER OF PARALLEL PROGRAM VARIANTS." Vestnik komp'iuternykh i informatsionnykh tekhnologii, no. 183 (September 2019): 43–49. http://dx.doi.org/10.14489/vkit.2019.09.pp.043-049.

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In this paper, we review and compare the methods of parallel applications’ development based on the automatic program parallelizing for computer systems with shared and distributed memory and on the information graph’s hardware costs and performance reduction for reconfigurable computer systems. The increase in the number of computer system’s units or in the problem’s dimension leads to the significant growth of the automatic parallelization complexity for a procedural program. As a result, the obtainment of parallelizing results in acceptable time using state-of-the-art computer systems is ve

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Windsteiger, Wolfgang. "An automated prover for Zermelo–Fraenkel set theory in Theorema." Journal of Symbolic Computation 41, no. 3-4 (2006): 435–70. http://dx.doi.org/10.1016/j.jsc.2005.04.013.

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Pelletier, Francis Jeffry. "Seventy-five problems for testing automatic theorem provers." Journal of Automated Reasoning 2, no. 2 (1986): 191–216. http://dx.doi.org/10.1007/bf02432151.

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Cordero, P., G. Gutiérrez, J. Martínez, and I. P. de Guzmán. "A New Algebraic Tool for Automatic Theorem Provers." Annals of Mathematics and Artificial Intelligence 42, no. 4 (2004): 369–98. http://dx.doi.org/10.1023/b:amai.0000038312.77514.3c.

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Bundy, Alan. "Automated theorem provers: a practical tool for the working mathematician?" Annals of Mathematics and Artificial Intelligence 61, no. 1 (2011): 3–14. http://dx.doi.org/10.1007/s10472-011-9248-8.

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Yang, Wonsuk, Hancheol Park, and Jong C. Park. "Neural Theorem Prover with Word Embedding for Efficient Automatic Annotation." Journal of KIISE 44, no. 4 (2017): 399–410. http://dx.doi.org/10.5626/jok.2017.44.4.399.

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Akbarpour, Behzad, and Lawrence Charles Paulson. "MetiTarski: An Automatic Theorem Prover for Real-Valued Special Functions." Journal of Automated Reasoning 44, no. 3 (2009): 175–205. http://dx.doi.org/10.1007/s10817-009-9149-2.

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