{"title":"Polygraphic programs and polynomial-time functions","authors":"Guillaume Bonfante, Yves Guiraud","doi":"10.2168/LMCS-5(2:14)2009","DOIUrl":null,"url":null,"abstract":"We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a Turing-complete computational model. Their algebraic structure is used by analysis tools, called polygraphic interpretations, for complexity analysis. In particular, we delineate a subclass of polygraphic programs that compute exactly the functions that are Turing-computable in polynomial time.","PeriodicalId":49904,"journal":{"name":"Logical Methods in Computer Science","volume":"5 1","pages":"1-37"},"PeriodicalIF":0.6000,"publicationDate":"2007-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Logical Methods in Computer Science","FirstCategoryId":"94","ListUrlMain":"https://doi.org/10.2168/LMCS-5(2:14)2009","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 13
Abstract
We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a Turing-complete computational model. Their algebraic structure is used by analysis tools, called polygraphic interpretations, for complexity analysis. In particular, we delineate a subclass of polygraphic programs that compute exactly the functions that are Turing-computable in polynomial time.
期刊介绍：
Logical Methods in Computer Science is a fully refereed, open access, free, electronic journal. It welcomes papers on theoretical and practical areas in computer science involving logical methods, taken in a broad sense; some particular areas within its scope are listed below. Papers are refereed in the traditional way, with two or more referees per paper. Copyright is retained by the author.
Topics of Logical Methods in Computer Science:
Algebraic methods
Automata and logic
Automated deduction
Categorical models and logic
Coalgebraic methods
Computability and Logic
Computer-aided verification
Concurrency theory
Constraint programming
Cyber-physical systems
Database theory
Defeasible reasoning
Domain theory
Emerging topics: Computational systems in biology
Emerging topics: Quantum computation and logic
Finite model theory
Formalized mathematics
Functional programming and lambda calculus
Inductive logic and learning
Interactive proof checking
Logic and algorithms
Logic and complexity
Logic and games
Logic and probability
Logic for knowledge representation
Logic programming
Logics of programs
Modal and temporal logics
Program analysis and type checking
Program development and specification
Proof complexity
Real time and hybrid systems
Reasoning about actions and planning
Satisfiability
Security
Semantics of programming languages
Term rewriting and equational logic
Type theory and constructive mathematics.
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