NP-Completeness Results for Deductive Problems on Stratified Terms

Tour, Thierry Boy de la; Echenim, Mnacho

doi:10.1007/978-3-540-39813-4_23

Cited by 4 publications

(6 citation statements)

References 7 publications

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“…So far we have proved that problems 1 to 5 are more difficult than G_CSTR, and we have proved in [7] that G_CSTR is NP-hard, and therefore so are these five problems. The proof in [7] is quite complex, however, and we have found a simpler one.…”

Section: Np-hardness Of Group Constraintsmentioning

confidence: 94%

“…In Sections 2 and 3 (adapted from [6] and [7]), we present the way terms are represented in term graph rewriting, and we focus on those graphs that have a treelike structure. We construct our own version of the stratified terms of [1] and obtain stratified term trees, from which we construct a permutation group on vertices and an action of this group on stratified term trees.…”

Section: Permutation Groups On Term Graphsmentioning

confidence: 99%

“…We have already obtained NP-completeness results for these problems on unrestricted stratified term trees in [7], but the term trees used in some proofs seemed rather unnatural, and certainly not the kind that could reasonably exist in a theorem prover. Hence, the current restriction seems more significant to us.…”

Section: Deductive Problemsmentioning

confidence: 99%

“…Problem 5 appears to be more complex, but we can still bound it at the second level of the polynomial hierarchy; see [11] or [14]. The following result is from [7].…”

Section: T ∈ S[t ] ⇔ ∃σ ∈ G T Such That T = τ (Um(t σ ))mentioning

confidence: 99%

“…As in [7] we now work on group constraints, by which we mean the following problem. We now prove that such group constraints can be solved as a membership problem on quite simple scs-term trees.…”

Section: From Stratified Sets To Group Constraintsmentioning

confidence: 99%

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On the Complexity of Deduction Modulo Leaf Permutative Equations

Tour¹,

Echenim²

2004

J Autom Reasoning

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In the context of equational reasoning, J. Avenhaus and D. Plaisted proposed to deal with leaf permutative equations in a uniform, specialized way. The simplicity of these equations and the useless variations that they produce are good incentives to lift theorem proving to so-called stratified terms, in order to perform deduction modulo such equations. This requires specialized algorithms for standard problems involved in automated deduction. To analyze the computational complexity of these problems, we focus on the group theoretic properties of stratified terms. NP-completeness results are given and (slightly) relieved by restrictions on leaf permutative theories, which allow the use of techniques from computational group theory.

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Section: Np-hardness Of Group Constraintsmentioning

confidence: 94%

Section: Permutation Groups On Term Graphsmentioning

confidence: 99%

Section: Deductive Problemsmentioning

confidence: 99%

“…Problem 5 appears to be more complex, but we can still bound it at the second level of the polynomial hierarchy; see [11] or [14]. The following result is from [7].…”

Section: T ∈ S[t ] ⇔ ∃σ ∈ G T Such That T = τ (Um(t σ ))mentioning

confidence: 99%

Section: From Stratified Sets To Group Constraintsmentioning

confidence: 99%

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