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Memoization for Unary Logic Programming: Characterizing PTIME [article]

Clément Aubert
2015 arXiv   pre-print
As an application of our techniques, we show a PTIME-completeness result for a class of logic programming queries which use only unary function symbols.  ...  We then introduce an algebraic counterpart of the memoization technique in order to show its PTIME soundness. We finally relate our approach and complexity results to complexity of logic programming.  ...  This allows us to show that the combined complexity problem for unary logic program is PTIME-complete. As an illustration, we show in Sect.  ... 
arXiv:1501.05104v2 fatcat:272rdzkgdjay5dozgcfuotkwym

Unary Resolution: Characterizing Ptime [chapter]

Clément Aubert, Marc Bagnol, Thomas Seiller
2016 Lecture Notes in Computer Science  
As a direct consequence, we get a Ptime-completeness result for a class of logic programming queries that uses only unary function symbols.  ...  More precisely, we restrict this framework to terms (logic programs, rewriting rules) using only unary symbols.  ...  Cook's memoization technique [15] , that proves that any such unary logic program can be decided in polynomial time.  ... 
doi:10.1007/978-3-662-49630-5_22 fatcat:44jk7rigrfaxplojjlzxshhveu

Observation of implicit complexity by non confluence

Guillaume Bonfante
2010 Electronic Proceedings in Theoretical Computer Science  
We come back to some well known classes of first-order functional program, for which we have a characterization of their intentional properties, namely the class of cons-free programs, the class of programs  ...  They all correspond to PTIME. We prove that adding non confluence to the rules leads to respectively PTIME, NPTIME and PSPACE.  ...  I'd like to thank the anonymous referees for their precious help. Their sharp reading has been largely valuable to rewrite some part of the draft.  ... 
doi:10.4204/eptcs.23.2 fatcat:aixersmuvzct3ag3luxe3zgwku

On The Resolution Semiring

Marc Bagnol
2014 Zenodo  
In this thesis, we study a semiring structure with a product based on theresolution rule of logic programming.  ...  in the semiring we study is undecidable in general, it willappear that certain restrictions allow for characterizations of (deterministicand non-deterministic) logarithmic space and (deterministic) polynomial  ...  the characterizations of Logspace, NLogspace and Ptime in the next sections.  ... 
doi:10.5281/zenodo.806771 fatcat:klgfbxmvfrf3xhad2pb4tq56ee

Design and Implementation of the LogicBlox System

Molham Aref, Balder ten Cate, Todd J. Green, Benny Kimelfeld, Dan Olteanu, Emir Pasalic, Todd L. Veldhuizen, Geoffrey Washburn
2015 Proceedings of the 2015 ACM SIGMOD International Conference on Management of Data - SIGMOD '15  
facilities; a novel concurrency control scheme; and built-in support for prescriptive and predictive analytics.  ...  These include: LogiQL, a unified and declarative language based on Datalog; the use of purely functional data structures; novel join processing strategies; advanced incremental maintenance and live programming  ...  LFTJ for unary predicates. We first describe how LFTJ works for the special case of joining unary predicates A 1 (x), . . . , A k (x).  ... 
doi:10.1145/2723372.2742796 dblp:conf/sigmod/ArefCGKOPVW15 fatcat:rsqnraye3ncz7chrc6ofqwy7ii

Unification and Logarithmic Space [chapter]

Clément Aubert, Marc Bagnol
2014 Lecture Notes in Computer Science  
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification.  ...  We then prove that whether an observation (the algebraic counterpart of a program) accepts a word can be decided within logarithmic space.  ...  The authors would like to thanks Jean-Yves Girard for inspiring hints he gave us during the writing of this article.  ... 
doi:10.1007/978-3-319-08918-8_6 fatcat:yid3scdrsvdktlufecrnnrpqum

Unification and Logarithmic Space [article]

Clément Aubert, Marc Bagnol
2018 arXiv   pre-print
We present an algebraic characterization of the complexity classes Logspace and Nlogspace, using an algebra with a composition law based on unification.  ...  This new bridge between unification and complexity classes is rooted in proof theory and more specifically linear logic and geometry of interaction.  ...  The authors would like to thanks Jean-Yves Girard for inspiring hints he gave us during the writing of this article.  ... 
arXiv:1805.11988v1 fatcat:sujxkud2znahpp2qs5fptdim2q

First- and Second-Order Models of Recursive Arithmetics [article]

Ján Kľuka, Paul J. Voda
2017 arXiv   pre-print
We introduce and study first- and second-order theories of recursive arithmetic ARA_1 and ARA_2 capable of characterizing various computational complexity classes and based on function algebras A, studied  ...  We have been using the language (which comes with an integrated theorem prover for PA) in courses teaching computer programming and program verification for the last twenty years [23] .  ...  We will see below that the algebra  ( ) is suitable for the characterization of space complexity classes.  ... 
arXiv:1705.05459v1 fatcat:fsiz2psexzdrlpkpxwlxy3co5m

Algorithmic aspects of type-based program synthesis

Andrej Dudenhefner, Technische Universität Dortmund, Technische Universität Dortmund
Inhabitation in typed lambda-calculi can be seen as functional program synthesis from scratch. Complementarily, inhabitation in combinatory logic can be seen as domain-specific program synthesis.  ...  , (o+2)-ExpTime-completeness of inhabitation in combinatory logic with intersection types with instantiation of bounded order o, and ExpTime-hardness of intersection type unification.  ...  We considered typed λ-calculi for program synthesis from scratch and typed combinatory logic for domain-specific program synthesis.  ... 
doi:10.17877/de290r-20108 fatcat:eizzv5sgwrgl3os5bal27h437q

Complexity Hierarchies and Higher-order Cons-free Term Rewriting [article]

Cynthia Kop, Jakob Grue Simonsen
2017 arXiv   pre-print
the class PTIME.  ...  In programming language research, cons-free languages have been used to characterize hierarchies of computational complexity classes; in term rewriting, cons-free first-order TRSs have been used to characterize  ...  PTIME.  ... 
arXiv:1611.10334v2 fatcat:6icowhvkqffcbjxdwvlqsax3eq

Max-Plus Quasi-interpretations [chapter]

Roberto M. Amadio
2003 Lecture Notes in Computer Science  
We prove that in this case the synthesis problem is NP-hard, and in NP for the particular case of multi-linear quasi-interpretations when programs are specified by rules of bounded size.  ...  Quasi-interpretations are a tool to bound the size of the values computed by a first-order functional program (or a term rewriting system) and thus a mean to extract bounds on its computational complexity  ...  By imposing further conditions on the termination method (product path-order) it is also possible to characterize Ptime [Mar00] .  ... 
doi:10.1007/3-540-44904-3_3 fatcat:buxjofnbhvc2dmhwqfkwkwx5ye