Graph transformation theory relies upon the composition of rules to express the effects of sequences of rules. In practice, graphs are often subject to constraints, ruling out many candidates for composed rules. Focusing on the case of sesqui-pushout (SqPO) semantics, we develop a number of alternative strategies for computing compositions, each theoretically and with an implementation via the Python API of the Z3 theorem prover. The strategies comprise a straightforward generate-and-test strategy based on forbidden graph patterns, a variant with a more implicit logical encoding of the negative constraints, and a modular strategy, where the patterns are decomposed as forbidden relation patterns. For a toy model of polymer formation in organic chemistry, we compare the performance of the three strategies in terms of execution times and memory consumption.
{"title":"Efficient Computation of Graph Overlaps for Rule Composition: Theory and Z3 Prototyping","authors":"Nicolas Behr, R. Heckel, Maryam Ghaffari Saadat","doi":"10.4204/eptcs.330.8","DOIUrl":"https://doi.org/10.4204/eptcs.330.8","url":null,"abstract":"Graph transformation theory relies upon the composition of rules to express the effects of sequences of rules. In practice, graphs are often subject to constraints, ruling out many candidates for composed rules. Focusing on the case of sesqui-pushout (SqPO) semantics, we develop a number of alternative strategies for computing compositions, each theoretically and with an implementation via the Python API of the Z3 theorem prover. The strategies comprise a straightforward generate-and-test strategy based on forbidden graph patterns, a variant with a more implicit logical encoding of the negative constraints, and a modular strategy, where the patterns are decomposed as forbidden relation patterns. For a toy model of polymer formation in organic chemistry, we compare the performance of the three strategies in terms of execution times and memory consumption.","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125423428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-10-28DOI: 10.20944/PREPRINTS202010.0584.V1
A. Sarkar, Z. Al-Ars, K. Bertels
In this article we explore the limiting behavior of the universal prior distribution applied over multiple meta-level hierarchy of program and output data of a Turing machine. We were motivated to reduce the effect of Solomonoff's assumption that all computable functions/hypothesis of the same length are equally likely, by weighing each program in turn by the algorithmic probability of their description number encoding. In the limiting case we converge the set of all possible program strings of a fixed-length to a distribution of self-replicating quines and quine-relays - having the structure of a constructor. We discuss how experimental algorithmic information theory provides insights towards understanding the fundamental metrics proposed in this work and reflect on the significance of these result in the constructor theory of life.
{"title":"Quines are the Fittest Programs - Large Nesting Algorithmic Probability Converges to Constructors","authors":"A. Sarkar, Z. Al-Ars, K. Bertels","doi":"10.20944/PREPRINTS202010.0584.V1","DOIUrl":"https://doi.org/10.20944/PREPRINTS202010.0584.V1","url":null,"abstract":"In this article we explore the limiting behavior of the universal prior distribution applied over multiple meta-level hierarchy of program and output data of a Turing machine. We were motivated to reduce the effect of Solomonoff's assumption that all computable functions/hypothesis of the same length are equally likely, by weighing each program in turn by the algorithmic probability of their description number encoding. In the limiting case we converge the set of all possible program strings of a fixed-length to a distribution of self-replicating quines and quine-relays - having the structure of a constructor. We discuss how experimental algorithmic information theory provides insights towards understanding the fundamental metrics proposed in this work and reflect on the significance of these result in the constructor theory of life.","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122721285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This volume contains the proceedings of the 14th International Conference on Quantum Physics and Logic (QPL 2017), which was held July 3-7, 2017 at the LUX Cinema Nijmegen, the Netherlands, and was hosted by Radboud University. QPL is a conference that brings together researchers working on mathematical foundations of quantum physics, quantum computing, and related areas, with a focus on structural perspectives and the use of logical tools, ordered algebraic and category-theoretic structures, formal languages, semantical methods, and other computer science techniques applied to the study of physical behaviour in general. This conference also welcomes work that applies structures and methods inspired by quantum theory to other fields (including computer science).
{"title":"Proceedings 14th International Conference on Quantum Physics and Logic","authors":"B. Coecke, A. Kissinger","doi":"10.4204/EPTCS.266","DOIUrl":"https://doi.org/10.4204/EPTCS.266","url":null,"abstract":"This volume contains the proceedings of the 14th International Conference on Quantum Physics and Logic (QPL 2017), which was held July 3-7, 2017 at the LUX Cinema Nijmegen, the Netherlands, and was hosted by Radboud University. QPL is a conference that brings together researchers working on mathematical foundations of quantum physics, quantum computing, and related areas, with a focus on structural perspectives and the use of logical tools, ordered algebraic and category-theoretic structures, formal languages, semantical methods, and other computer science techniques applied to the study of physical behaviour in general. This conference also welcomes work that applies structures and methods inspired by quantum theory to other fields (including computer science).","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132133105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional language. We develop a theory of higher order functions that is well-suited for the complexity analysis of this programming language. The interpretation domain is a complete lattice and, consequently, we express program interpretation in terms of a least fixpoint. As an application, by bounding interpretations by higher order polynomials, we characterize Basic Feasible Functions at any order.
{"title":"Theory of higher order interpretations and application to Basic Feasible Functions.","authors":"Emmanuel Hainry, Romain Péchoux","doi":"10.2168/LMCS-","DOIUrl":"https://doi.org/10.2168/LMCS-","url":null,"abstract":"Interpretation methods and their restrictions to polynomials have been deeply used to control the termination and complexity of first-order term rewrite systems. This paper extends interpretation methods to a pure higher order functional language. We develop a theory of higher order functions that is well-suited for the complexity analysis of this programming language. The interpretation domain is a complete lattice and, consequently, we express program interpretation in terms of a least fixpoint. As an application, by bounding interpretations by higher order polynomials, we characterize Basic Feasible Functions at any order.","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"11 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133072676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This volume contains the formal proceedings of the 4th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2017), held on 8th September 2017 in Oxford, United Kingdom, and affiliated with the Second International Conference on Formal Structures for Computation and Deduction (FSCD 2017).
{"title":"Proceedings Fourth International Workshop on Rewriting Techniques for Program Transformations and Evaluation","authors":"Horatiu Cirstea, Santiago Escobar","doi":"10.4204/EPTCS.235","DOIUrl":"https://doi.org/10.4204/EPTCS.235","url":null,"abstract":"This volume contains the formal proceedings of the 4th International Workshop on Rewriting Techniques for Program Transformations and Evaluation (WPTE 2017), held on 8th September 2017 in Oxford, United Kingdom, and affiliated with the Second International Conference on Formal Structures for Computation and Deduction (FSCD 2017).","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121152505","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The SYNT workshop aims to bring together researchers interested in the broad area of synthesis of computing systems. The goal is to foster the development of frontier techniques in automating the development of computing system. Contributions of interest include algorithms, complexity and decidability analysis, as well as reproducible heuristics, implemented tools, and experimental evaluation. Application domains include software, hardware, embedded, and cyberphysical systems. Computation models include functional, reactive, hybrid and timed systems. Identifying, formalizing, and evaluating synthesis in particular application domains is encouraged. The fifth iteration of the workshop took place in Toronto, Canada. It was co-located with the 28th International Conference on Computer Aided Verification. The workshop included twelve contributed talks and two invited talks. In addition, it featured a special session about the Syntax-Guided Synthesis Competition (SyGuS) and the SyntComp Synthesis competition.
{"title":"Proceedings Fifth Workshop on Synthesis","authors":"R. Piskac, Rayna Dimitrova","doi":"10.4204/EPTCS.229","DOIUrl":"https://doi.org/10.4204/EPTCS.229","url":null,"abstract":"The SYNT workshop aims to bring together researchers interested in the broad area of synthesis of computing systems. The goal is to foster the development of frontier techniques in automating the development of computing system. Contributions of interest include algorithms, complexity and decidability analysis, as well as reproducible heuristics, implemented tools, and experimental evaluation. Application domains include software, hardware, embedded, and cyberphysical systems. Computation models include functional, reactive, hybrid and timed systems. Identifying, formalizing, and evaluating synthesis in particular application domains is encouraged. \u0000The fifth iteration of the workshop took place in Toronto, Canada. It was co-located with the 28th International Conference on Computer Aided Verification. The workshop included twelve contributed talks and two invited talks. In addition, it featured a special session about the Syntax-Guided Synthesis Competition (SyGuS) and the SyntComp Synthesis competition.","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117058337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The workshop series intends to cover research that investigates the computational aspects of classical logic and mathematics. Its focus is on unwinding the computational content of logical principles and proof in mathematics based on these principles, aiming to bring together researchers from both fields and exchange ideas. Classical Logic and Computation (CL&C) 2016 was the sixth edition of this workshop series held as a satellite to FSCD 2016 on June 23, 2016 in Porto, Portugal. In this sixth edition we received 11 submissions of both short and full papers. Eight (8) of these were selected to present at the meeting in Porto, and five (5) full papers were initially accepted to appear at this EPTCS special volume of which one was subsequently withdrawn by its authors. An invited talk was given by Marc Bezem (U. of Bergen): Coherent Logic - an overview. Other topics covered by this years submissions included: computational content of proofs using nonstandard analysis, a structured grammar-based approach to the Herbrand content of proofs, semantics of the lambda-mu calculus, normalization of classical natural deduction proofs, proof mining of noneffective proofs in convex optimization and algebra by functional interpretations. I like to thank the members of the program committee for their excellent work: Steffen van Bakel (London), Stefano Berardi (Torino), Fernando Ferreira (Lisboa), Hugo de'Liguoro (Torino), Alexandre Miquel (Montevideo). Ulrich Kohlenbach (Darmstadt, PC Chair)
{"title":"Proceedings Seventh International Workshop on Classical Logic and Computation","authors":"U. Kohlenbach, S. V. Bakel, S. Berardi","doi":"10.4204/EPTCS.213","DOIUrl":"https://doi.org/10.4204/EPTCS.213","url":null,"abstract":"The workshop series intends to cover research that investigates the computational aspects of classical logic and mathematics. Its focus is on unwinding the computational content of logical principles and proof in mathematics based on these principles, aiming to bring together researchers from both fields and exchange ideas. \u0000Classical Logic and Computation (CL&C) 2016 was the sixth edition of this workshop series held as a satellite to FSCD 2016 on June 23, 2016 in Porto, Portugal. \u0000In this sixth edition we received 11 submissions of both short and full papers. Eight (8) of these were selected to present at the meeting in Porto, and five (5) full papers were initially accepted to appear at this EPTCS special volume of which one was subsequently withdrawn by its authors. An invited talk was given by Marc Bezem (U. of Bergen): Coherent Logic - an overview. Other topics covered by this years submissions included: computational content of proofs using nonstandard analysis, a structured grammar-based approach to the Herbrand content of proofs, semantics of the lambda-mu calculus, normalization of classical natural deduction proofs, proof mining of noneffective proofs in convex optimization and algebra by functional interpretations. I like to thank the members of the program committee for their excellent work: Steffen van Bakel (London), Stefano Berardi (Torino), Fernando Ferreira (Lisboa), Hugo de'Liguoro (Torino), Alexandre Miquel (Montevideo). \u0000Ulrich Kohlenbach (Darmstadt, PC Chair)","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129745641","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We are proud to present the papers from the 17th Refinement Workshop, co-located with FM 2015 held in Oslo, Norway on June 22nd, 2015. Refinement is one of the cornerstones of a formal approach to software engineering: the process of developing a more detailed design or implementation from an abstract specification through a sequence of mathematically-based steps that maintain correctness with respect to the original specification. This 17th workshop continued a 20+ year tradition under the auspices of the British Computer Society (BCS) FACS special interest group. This is the third volume that has appeared as an EPTCS proceedings, and we would like to thank the editorial board (and in particular Rob van Glabbeek) for their help and cooperation in making this happen. The organisers would like to thank everyone: the authors, BCS-FACS, EPTCS, and the organisers of FM 2015 for their help in organising this workshop, the participants of the workshop, and the reviewers involved in selecting the papers.
2015年6月22日，我们在挪威奥斯陆与fm2015共同举办了第17届改进研讨会。精化是软件工程形式化方法的基石之一:从抽象规范通过一系列基于数学的步骤开发更详细的设计或实现的过程，这些步骤保持了相对于原始规范的正确性。在英国计算机协会(BCS) FACS特别兴趣小组的主持下，第17届研讨会延续了20多年的传统。这是EPTCS论文集的第三卷，我们要感谢编委会(特别是Rob van Glabbeek)的帮助和合作。组织者在此感谢所有人:作者、BCS-FACS、EPTCS和fm2015的组织者，感谢他们帮助组织这次研讨会，感谢研讨会的参与者，以及参与论文选择的审稿人。
{"title":"Proceedings 17th International Workshop on Refinement","authors":"J. Derrick, E. Boiten, S. Reeves","doi":"10.4204/EPTCS.209","DOIUrl":"https://doi.org/10.4204/EPTCS.209","url":null,"abstract":"We are proud to present the papers from the 17th Refinement Workshop, co-located with FM 2015 held in Oslo, Norway on June 22nd, 2015. \u0000Refinement is one of the cornerstones of a formal approach to software engineering: the process of developing a more detailed design or implementation from an abstract specification through a sequence of mathematically-based steps that maintain correctness with respect to the original specification. \u0000This 17th workshop continued a 20+ year tradition under the auspices of the British Computer Society (BCS) FACS special interest group. \u0000This is the third volume that has appeared as an EPTCS proceedings, and we would like to thank the editorial board (and in particular Rob van Glabbeek) for their help and cooperation in making this happen. \u0000The organisers would like to thank everyone: the authors, BCS-FACS, EPTCS, and the organisers of FM 2015 for their help in organising this workshop, the participants of the workshop, and the reviewers involved in selecting the papers.","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124990578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-10-29DOI: 10.2168/LMCS-12(3:12)2016
G. Japaridze
Clarithmetics are number theories based on computability logic (see this http URL ). Formulas of these theories represent interactive computational problems, and their "truth" is understood as existence of an algorithmic solution. Various complexity constraints on such solutions induce various versions of clarithmetic. The present paper introduces a parameterized/schematic version CLA11(P1,P2,P3,P4). By tuning the three parameters P1,P2,P3 in an essentially mechanical manner, one automatically obtains sound and complete theories with respect to a wide range of target tricomplexity classes, i.e. combinations of time (set by P3), space (set by P2) and so called amplitude (set by P1) complexities. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a solution from the given tricomplexity class and, furthermore, such a solution can be automatically extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a solution from the given tricomplexity class is represented by some theorem of the system. Furthermore, through tuning the 4th parameter P4, at the cost of sacrificing recursive axiomatizability but not simplicity or elegance, the above extensional completeness can be strengthened to intensional completeness, according to which every formula representing a problem with a solution from the given tricomplexity class is a theorem of the system. This article is published in two parts. The previous Part I has introduced the system and proved its completeness, while the present Part II is devoted to proving soundness.
{"title":"Build your own clarithmetic II: Soundness","authors":"G. Japaridze","doi":"10.2168/LMCS-12(3:12)2016","DOIUrl":"https://doi.org/10.2168/LMCS-12(3:12)2016","url":null,"abstract":"Clarithmetics are number theories based on computability logic (see this http URL ). Formulas of these theories represent interactive computational problems, and their \"truth\" is understood as existence of an algorithmic solution. Various complexity constraints on such solutions induce various versions of clarithmetic. The present paper introduces a parameterized/schematic version CLA11(P1,P2,P3,P4). By tuning the three parameters P1,P2,P3 in an essentially mechanical manner, one automatically obtains sound and complete theories with respect to a wide range of target tricomplexity classes, i.e. combinations of time (set by P3), space (set by P2) and so called amplitude (set by P1) complexities. Sound in the sense that every theorem T of the system represents an interactive number-theoretic computational problem with a solution from the given tricomplexity class and, furthermore, such a solution can be automatically extracted from a proof of T. And complete in the sense that every interactive number-theoretic problem with a solution from the given tricomplexity class is represented by some theorem of the system. Furthermore, through tuning the 4th parameter P4, at the cost of sacrificing recursive axiomatizability but not simplicity or elegance, the above extensional completeness can be strengthened to intensional completeness, according to which every formula representing a problem with a solution from the given tricomplexity class is a theorem of the system. This article is published in two parts. The previous Part I has introduced the system and proved its completeness, while the present Part II is devoted to proving soundness.","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134003546","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-10-28DOI: 10.2168/LMCS-11(4:15)2015
Drewes Frank, Leroux J'erome
A Petri net is structurally cyclic if every configuration is reachable from itself in one or more steps. We show that structural cyclicity is decidable in deterministic polynomial time. For this, we adapt the Kosaraju's approach for the general reachability problem for Petri nets.
{"title":"Structurally Cyclic Petri Nets","authors":"Drewes Frank, Leroux J'erome","doi":"10.2168/LMCS-11(4:15)2015","DOIUrl":"https://doi.org/10.2168/LMCS-11(4:15)2015","url":null,"abstract":"A Petri net is structurally cyclic if every configuration is reachable from itself in one or more steps. We show that structural cyclicity is decidable in deterministic polynomial time. For this, we adapt the Kosaraju's approach for the general reachability problem for Petri nets.","PeriodicalId":148456,"journal":{"name":"arXiv: Logic in Computer Science","volume":"87 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115114416","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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