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Ground reducibility and automata with disequality constraints
[chapter]

1994
*
Lecture Notes in Computer Science
*

Using the

doi:10.1007/3-540-57785-8_138
fatcat:z6pkieo5fzge3l3q7fzh3ohhhy
*automata**with**constraints*, we give an algorithm for the decision of*ground**reducibility*of a term t w.r.t. a rewriting system R. ... The complexity of the algorithm is doubly exponential in the maximum of the depths of t*and*R*and*the cardinal of R. 3 J J J J J J J J J J J J ...*Automata**with**disequality**constraints*(ADC) We assume in this section that A = (Q; Q f ; P) is a CA without equality*constraints*. We call this kind of*constrainted**automata*ADC for short. ...##
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Extending ${\cal H}_1$ -Clauses with Path Disequalities
[chapter]

2012
*
Lecture Notes in Computer Science
*

We extend H1-clauses

doi:10.1007/978-3-642-28729-9_11
fatcat:x7cbmhuc7zd5fnhg46aipiwyj4
*with**disequalities*between paths. ... We show that the extended clauses can be normalized into an equivalent tree automaton*with*path*disequalities**and*therefore conclude that satisfiability of conjunctive queries to predicates defined by ... We thank Florent Jacquemard for a lively discussion, many helpful remarks*and*in particular, for pointing out reference [5] . ...##
###
Ground reducibility is EXPTIME-complete

2003
*
Information and Computation
*

It is more difficult to show that

doi:10.1016/s0890-5401(03)00134-2
fatcat:7u4gfjj6wnajngcs45clexu6ce
*ground**reducibility*belongs to DEXPTIME. We associate first an automaton*with**disequality**constraints*A R,t to a rewrite system R*and*a term t. ... Thanks to these lemmas, we can show that emptiness for an automaton*with**disequality**constraints*can be decided in a time which is polynomial in the number of states*and*exponential in the size of the ... Acknowledgments The authors wish to thank Bruce Reed for his proof of Theorem 32,*and*Denis Lugiez for his useful remarks*and*suggestions. ...##
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Solving Constrained Horn Clauses over ADTs by Finite Model Finding
[article]

2021
*
arXiv
*
pre-print

Thus we propose to represent program invariants regularly

arXiv:2108.00225v2
fatcat:skd33ohnwfhkjdrfqt2f3wyczi
*with*tree*automata*. We show how to automatically infer such regular invariants of ADT-manipulating programs using finite model finders. ... computation*and*their automatic construction is less expensive. ... For a CHC system , let ′ be a system*with*the*disequality**constraints*. ...##
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The HOM Problem is EXPTIME-Complete

2016
*
SIAM journal on computing (Print)
*

For example, tree

doi:10.1137/140999104
fatcat:yniqldd2wnegjfrgyuwxbmefjy
*automata**with*local*disequality**constraints*allowed proving EXPTIME-completeness of*ground**reducibility*[8], tree*automata**with**constraints*between brothers allowed proving decidability ... Tree*automata**with**disequality**and*implicit HOM equality*constraints*. ... To this end, we define a new class of tree*automata**with**constraints*called tree*automata**with**disequality**and*implicit HOM equality*constraints*(TA ihom, ≈ ). ...##
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The Recognizability Problem for Tree Automata with Comparisons between Brothers
[chapter]

1999
*
Lecture Notes in Computer Science
*

Several extensions of tree

doi:10.1007/3-540-49019-1_11
fatcat:74ijhgndincvxnzapwzt7trugq
*automata*have been de ned, in order to take in account non-linearity in terms. Roughly, these*automata*allow equality or*disequality**constraints*between subterms. ... Here we study this problem in the class REC6 = corresponding to comparisons between brothers*and*we prove its decidability. ... that there is no*disequality**constraint*between equal*ground*sons of the label. ...##
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Beyond the Elementary Representations of Program Invariants over Algebraic Data Types
[article]

2021
*
arXiv
*
pre-print

In this paper, we explore three different approaches to represent program invariants of ADT-manipulating programs: tree

arXiv:2104.04463v2
fatcat:nbk34cumzvg7xfemtfn4u6cole
*automata*,*and*first-order formulas*with*or without size*constraints*. ... In particular, program invariants represented by*automata*are capable of expressing more complex properties of computation*and*their automatic construction is often less expensive. ... For a CHC system , let ′ be a system*with**disequality**constraints*. ...##
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Asymmetric Unification and Disunification
[article]

2017
*
arXiv
*
pre-print

In Disunification we solve equations

arXiv:1706.05066v3
fatcat:fwhesedlwzh7zillg5ke7zdjfq
*and**disequations**with*respect to an equational theory for the case*with*free constants. ... We compare two kinds of unification problems: Asymmetric Unification*and*Disunification, which are variants of Equational Unification. ... to checking for*ground*solutions for a set of*disequations**and*equations. ...##
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Pumping, cleaning and symbolic constraints solving
[chapter]

1994
*
Lecture Notes in Computer Science
*

We de ne a new class of tree

doi:10.1007/3-540-58201-0_88
fatcat:n325gwiyrzcafjvfrf4jgdfiku
*automata*which generalizes both the encompassment*automata*of 3]*and*the*automata**with*tests between brothers of 2]. ... We give a pumping lemma for these*automata*, which implies that the emptiness of the corresponding language is decidable. ... Introduction*Ground**reducibility*of a term t*with*respect to a term rewriting system R is the property that all*ground*instances of t are*reducible*by R. ...##
###
Page 9198 of Mathematical Reviews Vol. , Issue 2004k
[page]

2004
*
Mathematical Reviews
*

To show that

*ground**reducibility*belongs to DEXPTIME, an automaton*with**disequal*- ity*constraints*Wg, is associated to a rewrite system &*and*a term t. ... This automaton is deterministic*and*accepts at least one term iff t is not*ground**reducible*by &. The number of states of Wg, is O(2'\! ...##
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Rigid Tree Automata
[chapter]

2009
*
Lecture Notes in Computer Science
*

Finally, a comparison of RTA

doi:10.1007/978-3-642-00982-2_38
fatcat:njyznxj3fvds3obgdaq646zlca
*with*several classes of tree*automata**with*local*and*global equality tests,*and**with*dag*automata*is also provided. ... This result, one of the first on rewrite closure of languages of tree*automata**with**constraints*, is enabling the extension of model checking procedures based on finite tree*automata*techniques. ... RTA are a particular case of the more general class Tree*Automata**with*General Equality*and**Disequality**constraints*(TAGED [4] ). ...##
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Sufficient completeness verification for conditional and constrained TRS

2012
*
Journal of Applied Logic
*

Our approach is integrated into a framework for inductive theorem proving based on tree grammars

doi:10.1016/j.jal.2011.09.001
fatcat:6ujglk45dra4pctmvfmzus7wba
*with**constraints*, a formalism which permits an exact representation of languages of*ground*constructor terms ... A precondition of one inference of this system refers to a (undecidable) property called strong*ground**reducibility*which is discharged to the above inductive theorem proving system. ... Acknowledgements We wish to sincerely thank Joe Hendrix for having processed the above examples of Sections 5*and*9*with*the Sufficient Completeness Checker for Maude,*and*the reviewers whose useful remarks ...##
###
TREE AUTOMATA WITH GLOBAL CONSTRAINTS

2010
*
International Journal of Foundations of Computer Science
*

A tree automaton

doi:10.1142/s012905411000743x
fatcat:c22olqcimvbunaaxntwxrzoqwy
*with*global tree equality*and**disequality**constraints*, TAGED for short, is an automaton on trees which allows to test (dis)equalities between subtrees which may be arbitrarily faraway. ... We give two applications of TAGEDs: decidability of an extension of Monadic Second Order Logic*with*tree isomorphism tests*and*of unification*with*membership*constraints*. ... These are tree*automata*A equipped*with*an equality = A*and*a*disequality*= A relation on (a subset of) states. ...##
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Goal-Directed Completion using SOUR Graphs
[chapter]

1997
*
Lecture Notes in Computer Science
*

The second phase starts

doi:10.1007/3-540-62950-5_58
fatcat:uopp3mdgyjhsfpykpajfenljie
*with*the goal solutions*and*works its way back to the original equations, solving*constraints*along the way. ... The rst phase, which runs in polynomial time, compiles the equations*and*the goal into a constrained tree*automata*representing the completed system,*and*a set of*constraints*representing goal solutions ... A constrained term, (or equation or*disequation*) t ' ] ] is a pair of a term (or equation or*disequation*) t*and*a*constraint*'. ...##
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The HOM problem is decidable

2013
*
Journal of the ACM
*

In a second step, we define a new class of

doi:10.1145/2508028.2501600
fatcat:pe7p526xjzg3dpzhbhdrv4zu3y
*automata**with**constraints*called tree*automata**with**disequality**and*HOM equality*constraints*, TA l 7 m o n for short. ... We also define a new class of*automata**with*arbitrary*disequality**constraints**and*a particular kind of equality*constraints*. ... For example, tree*automata**with*global*constraints*, which are similar to the equality*constraints*occurring in our TA U W V Y X in the sense that we impose equality of terms reaching identical (but local ...
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