Proof equivalence in MLL is PSPACE-complete

Heijltjes, Willem; Houston, Robin

doi:10.2168/lmcs-12(1:2)2016

Cited by 26 publications

(35 citation statements)

References 19 publications

(30 reference statements)

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“…Indeed, the Nondeterministic Constraint Logic construction of Hearn and Demaine [HD05], which gives a simple PSPACE-complete reconfiguration problem, allowed to show that many popular puzzles are PSPACE-complete [HD09;Meh14]. More interestingly, Heijltjes and Houston used the construction to prove that deciding the equivalence of proofs in a certain proof system is PSPACEcomplete [HH14], answering a question about normal forms of proofs that arose in this context.…”

Section: Figurementioning

confidence: 99%

Homomorphism Reconfiguration via Homotopy

Wrochna¹

2020

SIAM J. Discrete Math.

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For a fixed graph H, we consider the H-Recoloring problem : given a graph G and two H-colorings of G, i.e., homomorphisms from G to H, can one be transformed into the other by changing one color at a time, maintaining an H-coloring throughout. This is the same as finding a path in the Hom(G, H) complex. For H = K k this is the problem of finding paths between k-colorings, which was recently shown to be in P for k ≤ 3 and PSPACE-complete otherwise. We generalize the positive side of this dichotomy by providing an algorithm that solves the problem in polynomial time for any H with no C 4 subgraph. This gives a large class of constraints for which finding solutions to the Constraint Satisfaction Problem is NP-complete, but finding paths in the solution space is in P.The algorithm uses a characterization of possible reconfiguration sequences (paths in Hom(G, H)), whose main part is a purely topological condition described in terms of the fundamental groupoid of H seen as a topological space.

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Section: Figurementioning

confidence: 99%

Homomorphism Reconfiguration via Homotopy

Wrochna¹

2020

SIAM J. Discrete Math.

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“…The correctness of MALL proof nets was found to be NL-complete [9], but this appears not to impact the (much more restricted) purely additive fragment. Proof equivalence for MLL with units was recently shown to be PSPACE-complete, by Robin Houston and the first author [16].…”

Section: H Related Workmentioning

confidence: 99%

Complexity Bounds for Sum-Product Logic via Additive Proof Nets and Petri Nets

Heijltjes

Hughes

2015

2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science

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Abstract-We investigate efficient algorithms for the additive fragment of linear logic. This logic is an internal language for categories with finite sums and products, and describes concurrent two-player games of finite choice. In the context of session types, typing disciplines for communication along channels, the logic describes the communication of finite choice along a single channel.We give a simple linear time correctness criterion for unit-free propositional additive proof nets via a natural construction on Petri nets. This is an essential ingredient to linear time complexity of the second author's combinatorial proofs for classical logic.For full propositional additive linear logic, including the units, we give a proof search algorithm that is linear-time in the product of the source and target formula, and an algorithm for proof net correctness that is of the same time complexity. We prove that proof search in first-order additive linear logic is NP-complete.

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“…Adding multiplicative units while keep determinism is difficult, as their commuting conversion is subtle (e.g. conversion for MLL is PSPACE-complete [18]), and exhibit apparent nondeterminism. For instance the following proofs are convertible in MLL: where a().…”

Section: Extensions and Related Workmentioning

confidence: 99%

Causality in Linear Logic

Castellan

Yoshida

2019

Lecture Notes in Computer Science

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Commuting conversions of Linear Logic induce a notion of dependency between rules inside a proof derivation: a rule depends on a previous rule when they cannot be permuted using the conversions. We propose a new interpretation of proofs of Linear Logic as causal invariants which captures exactly this dependency. We represent causal invariants using game semantics based on general event structures, carving out, inside the model of [6], a submodel of causal invariants. This submodel supports an interpretation of unit-free Multiplicative Additive Linear Logic with MIX (MALL − ) which is (1) fully complete: every element of the model is the denotation of a proof and (2) injective: equality in the model characterises exactly commuting conversions of MALL − . This improves over the standard fully complete game semantics model of MALL − .

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Proof equivalence in MLL is PSPACE-complete

Cited by 26 publications

References 19 publications

Homomorphism Reconfiguration via Homotopy

Homomorphism Reconfiguration via Homotopy

Complexity Bounds for Sum-Product Logic via Additive Proof Nets and Petri Nets

Causality in Linear Logic

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