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Ground reducibility and automata with disequality constraints [chapter]

Hubert Comon, Florent Jacquemard
1994 Lecture Notes in Computer Science  
Using the 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.  ... 
doi:10.1007/3-540-57785-8_138 fatcat:z6pkieo5fzge3l3q7fzh3ohhhy

Extending ${\cal H}_1$ -Clauses with Path Disequalities [chapter]

Helmut Seidl, Andreas Reuß
2012 Lecture Notes in Computer Science  
We extend H1-clauses 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] .  ... 
doi:10.1007/978-3-642-28729-9_11 fatcat:x7cbmhuc7zd5fnhg46aipiwyj4

Ground reducibility is EXPTIME-complete

Hubert Comon, Florent Jacquemard
2003 Information and Computation  
It is more difficult to show that 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.  ... 
doi:10.1016/s0890-5401(03)00134-2 fatcat:7u4gfjj6wnajngcs45clexu6ce

Solving Constrained Horn Clauses over ADTs by Finite Model Finding [article]

Yurii Kostyukov, Dmitry Mordvinov, Grigory Fedyukovich
2021 arXiv   pre-print
Thus we propose to represent program invariants regularly 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.  ... 
arXiv:2108.00225v2 fatcat:skd33ohnwfhkjdrfqt2f3wyczi

The HOM Problem is EXPTIME-Complete

Carles Creus, Adrià Gascón, Guillem Godoy, Lander Ramos
2016 SIAM journal on computing (Print)  
For example, tree 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, ≈ ).  ... 
doi:10.1137/140999104 fatcat:yniqldd2wnegjfrgyuwxbmefjy

The Recognizability Problem for Tree Automata with Comparisons between Brothers [chapter]

Bruno Bogaert, Franck Seynhaeve, Sophie Tison
1999 Lecture Notes in Computer Science  
Several extensions of tree 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.  ... 
doi:10.1007/3-540-49019-1_11 fatcat:74ijhgndincvxnzapwzt7trugq

Beyond the Elementary Representations of Program Invariants over Algebraic Data Types [article]

Yurii Kostyukov, Dmitry Mordvinov, Grigory Fedyukovich
2021 arXiv   pre-print
In this paper, we explore three different approaches to represent program invariants of ADT-manipulating programs: tree 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.  ... 
arXiv:2104.04463v2 fatcat:nbk34cumzvg7xfemtfn4u6cole

Asymmetric Unification and Disunification [article]

Veena Ravishankar, Kimberly A. Gero, Paliath Narendran
2017 arXiv   pre-print
In Disunification we solve equations 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.  ... 
arXiv:1706.05066v3 fatcat:fwhesedlwzh7zillg5ke7zdjfq

Pumping, cleaning and symbolic constraints solving [chapter]

Anne -Cécile Caron, Hubert Comon, Jean -Luc Coquidé, Max Dauchet, Florent Jacquemard
1994 Lecture Notes in Computer Science  
We de ne a new class of tree 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.  ... 
doi:10.1007/3-540-58201-0_88 fatcat:n325gwiyrzcafjvfrf4jgdfiku

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'\!  ... 

Rigid Tree Automata [chapter]

Florent Jacquemard, Francis Klay, Camille Vacher
2009 Lecture Notes in Computer Science  
Finally, a comparison of RTA 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] ).  ... 
doi:10.1007/978-3-642-00982-2_38 fatcat:njyznxj3fvds3obgdaq646zlca

Sufficient completeness verification for conditional and constrained TRS

Adel Bouhoula, Florent Jacquemard
2012 Journal of Applied Logic  
Our approach is integrated into a framework for inductive theorem proving based on tree grammars 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  ... 
doi:10.1016/j.jal.2011.09.001 fatcat:6ujglk45dra4pctmvfmzus7wba

TREE AUTOMATA WITH GLOBAL CONSTRAINTS

EMMANUEL FILIOT, JEAN-MARC TALBOT, SOPHIE TISON
2010 International Journal of Foundations of Computer Science  
A tree automaton 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.  ... 
doi:10.1142/s012905411000743x fatcat:c22olqcimvbunaaxntwxrzoqwy

Goal-Directed Completion using SOUR Graphs [chapter]

Christopher Lynch
1997 Lecture Notes in Computer Science  
The second phase starts 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 '.  ... 
doi:10.1007/3-540-62950-5_58 fatcat:uopp3mdgyjhsfpykpajfenljie

The HOM problem is decidable

Guillem Godoy, Omer Giménez
2013 Journal of the ACM  
In a second step, we define a new class of 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  ... 
doi:10.1145/2508028.2501600 fatcat:pe7p526xjzg3dpzhbhdrv4zu3y
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