Logic Programming and Logarithmic Space

Aubert, Clément; Bagnol, Marc; Pistone, Paolo; Seiller, Thomas

doi:10.1007/978-3-319-12736-1_3

Cited by 8 publications

(25 citation statements)

References 29 publications

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“…Adding a "stack plugin" to observations extends modularly previous works [2,3,5,6] and gives the perfect tool to characterize Ptime. This modularity was inspired by the classical addition of a stack to an automaton, allowing to switch from Logspace to Ptime, and providing a decisive proof technique: memoizationor exponentiation by squaring in our context-implemented as saturation.…”

Section: Perspectivesmentioning

confidence: 89%

“…Definition 11 (observation semiring). We define the semirings P ⊥ of flows that do not use the symbols in P; and Σ lr the semiring generated by flows of the form c This simple restriction was shown to characterize (non-deterministic) logarithmic space computation [3,, with a natural subclass of balanced wirings corresponding to the deterministic case. The balanced restriction won't be further considered, even if previous results on the nilpotency problem for balanced wirings [3, p. 54], [8, Theorem IV.12] are required to complete the detailed proof of Theorem 5 [4,8].…”

Section: We Carry On the Convention Of Writingmentioning

confidence: 99%

“…We used in our previous work [3,6] the characterization of Logspace and NLogspace by 2-way k-head finite automata without pushdown stacks [43, pp. 223-225].…”

Section: Pushdown Automata and Ptime Completenessmentioning

confidence: 99%

“…Let us now consider the proof of Ptime-completeness for the set of balanced observations with stacks. It relies on an encoding that is similar to the previously developed encoding of 2-way k-head finite automata (without pushdown stack) by flows [3,Sect. 4.1].…”

Section: Pushdown Automata and Ptime Completenessmentioning

confidence: 99%

“…and offers a straightforward connection with complexity of logic programming [22]. Previous works in this direction led to characterizations of logarithmic space predicates Logspace and co-NLogspace [2,3], by considering restrictions on the height of variables.…”

Section: Introductionmentioning

confidence: 99%

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Unary Resolution: Characterizing Ptime

Aubert¹,

Bagnol²,

Seiller³

2016

Lecture Notes in Computer Science

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We give a characterization of deterministic polynomial time computation based on an algebraic structure called the resolution semiring, whose elements can be understood as logic programs or sets of rewriting rules over first-order terms. This construction stems from an interactive interpretation of the cut-elimination procedure of linear logic known as the geometry of interaction. This framework is restricted to terms (logic programs, rewriting rules) using only unary symbols, and this restriction is shown to be complete for polynomial time computation by encoding pushdown automata. Soundness w.r.t. Ptime is proven thanks to a saturation method similar to the one used for pushdown systems and inspired by the memoization technique. A Ptime-completeness result for a class of logic programming queries that uses only unary function symbols comes as a direct consequence.

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Section: Perspectivesmentioning

confidence: 89%

Section: We Carry On the Convention Of Writingmentioning

confidence: 99%

“…We used in our previous work [3,6] the characterization of Logspace and NLogspace by 2-way k-head finite automata without pushdown stacks [43, pp. 223-225].…”

Section: Pushdown Automata and Ptime Completenessmentioning

confidence: 99%

Section: Pushdown Automata and Ptime Completenessmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Unary Resolution: Characterizing Ptime

Aubert¹,

Bagnol²,

Seiller³

2016

Lecture Notes in Computer Science

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pymwp: A Static Analyzer Determining Polynomial Growth Bounds

Aubert,

Rubiano,

Rusch

et al. 2023

Automated Technology for Verification and Analysis

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We present pymwp, a static analyzer that automatically computes, if they exist, polynomial bounds relating input and output sizes. In case of exponential growth, our tool detects precisely which dependencies between variables induced it. Based on the sound mwp-flow calculus, the analysis captures bounds on large classes of programs by being non-deterministic and not requiring termination. For this reason, implementing this calculus required solving several non-trivial implementation problems, to handle its complexity and non-determinism, but also to provide meaningful feedback to the programmer. The duality of the analysis result and compositionality of the calculus make our approach original in the landscape of complexity analyzers. We conclude by demonstrating experimentally how pymwp is a practical and performant static analyzer to automatically evaluate variable growth bounds of C programs.

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Transcendental syntax I: deterministic case

Girard¹

2015

Math. Struct. Comp. Sci.

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Special Issue: Computing with lambda-terms. A special issue dedicated to Corrado Böhm for his 90th birthday.Thanks to Marc Bagnol, Paolo Pistone and Maria Rengo for their feedback.International audienceWe study logic in the light of the Kantian distinction between analytic (untyped, meaningless, locative) answers and synthetic (typed, meaningful, spiritual) questions. Which is specially relevant to proof-theory: in a proof-net, the upper part is locative, whereas the lower part is spiritual: a posteriori (explicit) as far as correctness is concerned, a priori (implicit) for questions dealing with consequence, typically cut-elimination. The divides locative/spiritual and explicit/implicit give rise to four blocks which are enough to explain the whole logical activity

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Logic Programming and Logarithmic Space

Cited by 8 publications

References 29 publications

Unary Resolution: Characterizing Ptime

Unary Resolution: Characterizing Ptime

pymwp: A Static Analyzer Determining Polynomial Growth Bounds

Transcendental syntax I: deterministic case

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