72,623 research outputs found
Infinite Runs in Abstract Completion
Completion is one of the first and most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In an earlier paper we presented a new and formalized correctness proof of abstract completion for finite runs. In this paper we extend our analysis and our formalization to infinite runs, resulting in a new proof that fair infinite runs produce complete presentations of the initial equations. We further consider ordered completion - an important extension of completion that aims to produce ground-complete presentations of the initial equations. Moreover, we revisit and extend results of Métivier concerning canonicity of rewrite systems. All proofs presented in the paper have been formalized in Isabelle/HOL
Constraint LTL Satisfiability Checking without Automata
This paper introduces a novel technique to decide the satisfiability of
formulae written in the language of Linear Temporal Logic with Both future and
past operators and atomic formulae belonging to constraint system D (CLTLB(D)
for short). The technique is based on the concept of bounded satisfiability,
and hinges on an encoding of CLTLB(D) formulae into QF-EUD, the theory of
quantifier-free equality and uninterpreted functions combined with D. Similarly
to standard LTL, where bounded model-checking and SAT-solvers can be used as an
alternative to automata-theoretic approaches to model-checking, our approach
allows users to solve the satisfiability problem for CLTLB(D) formulae through
SMT-solving techniques, rather than by checking the emptiness of the language
of a suitable automaton A_{\phi}. The technique is effective, and it has been
implemented in our Zot formal verification tool.Comment: 39 page
It Is NL-complete to Decide Whether a Hairpin Completion of Regular Languages Is Regular
The hairpin completion is an operation on formal languages which is inspired
by the hairpin formation in biochemistry. Hairpin formations occur naturally
within DNA-computing. It has been known that the hairpin completion of a
regular language is linear context-free, but not regular, in general. However,
for some time it is was open whether the regularity of the hairpin completion
of a regular language is is decidable. In 2009 this decidability problem has
been solved positively by providing a polynomial time algorithm. In this paper
we improve the complexity bound by showing that the decision problem is
actually NL-complete. This complexity bound holds for both, the one-sided and
the two-sided hairpin completions
Ten Conferences WORDS: Open Problems and Conjectures
In connection to the development of the field of Combinatorics on Words, we
present a list of open problems and conjectures that were stated during the ten
last meetings WORDS. We wish to continually update the present document by
adding informations concerning advances in problems solving
Finite-state Strategies in Delay Games (full version)
What is a finite-state strategy in a delay game? We answer this surprisingly
non-trivial question by presenting a very general framework that allows to
remove delay: finite-state strategies exist for all winning conditions where
the resulting delay-free game admits a finite-state strategy. The framework is
applicable to games whose winning condition is recognized by an automaton with
an acceptance condition that satisfies a certain aggregation property. Our
framework also yields upper bounds on the complexity of determining the winner
of such delay games and upper bounds on the necessary lookahead to win the
game. In particular, we cover all previous results of that kind as special
cases of our uniform approach
Reasoning with Forest Logic Programs and f-hybrid Knowledge Bases
Open Answer Set Programming (OASP) is an undecidable framework for
integrating ontologies and rules. Although several decidable fragments of OASP
have been identified, few reasoning procedures exist. In this article, we
provide a sound, complete, and terminating algorithm for satisfiability
checking w.r.t. Forest Logic Programs (FoLPs), a fragment of OASP where rules
have a tree shape and allow for inequality atoms and constants. The algorithm
establishes a decidability result for FoLPs. Although believed to be decidable,
so far only the decidability for two small subsets of FoLPs, local FoLPs and
acyclic FoLPs, has been shown. We further introduce f-hybrid knowledge bases, a
hybrid framework where \SHOQ{} knowledge bases and forest logic programs
co-exist, and we show that reasoning with such knowledge bases can be reduced
to reasoning with forest logic programs only. We note that f-hybrid knowledge
bases do not require the usual (weakly) DL-safety of the rule component,
providing thus a genuine alternative approach to current integration approaches
of ontologies and rules
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