150 research outputs found
A Perfect Model for Bounded Verification
A class of languages C is perfect if it is closed under Boolean operations
and the emptiness problem is decidable. Perfect language classes are the basis
for the automata-theoretic approach to model checking: a system is correct if
the language generated by the system is disjoint from the language of bad
traces. Regular languages are perfect, but because the disjointness problem for
CFLs is undecidable, no class containing the CFLs can be perfect.
In practice, verification problems for language classes that are not perfect
are often under-approximated by checking if the property holds for all
behaviors of the system belonging to a fixed subset. A general way to specify a
subset of behaviors is by using bounded languages (languages of the form w1*
... wk* for fixed words w1,...,wk). A class of languages C is perfect modulo
bounded languages if it is closed under Boolean operations relative to every
bounded language, and if the emptiness problem is decidable relative to every
bounded language.
We consider finding perfect classes of languages modulo bounded languages. We
show that the class of languages accepted by multi-head pushdown automata are
perfect modulo bounded languages, and characterize the complexities of decision
problems. We also show that bounded languages form a maximal class for which
perfection is obtained. We show that computations of several known models of
systems, such as recursive multi-threaded programs, recursive counter machines,
and communicating finite-state machines can be encoded as multi-head pushdown
automata, giving uniform and optimal underapproximation algorithms modulo
bounded languages.Comment: 14 pages, 6 figure
Queries with Guarded Negation (full version)
A well-established and fundamental insight in database theory is that
negation (also known as complementation) tends to make queries difficult to
process and difficult to reason about. Many basic problems are decidable and
admit practical algorithms in the case of unions of conjunctive queries, but
become difficult or even undecidable when queries are allowed to contain
negation. Inspired by recent results in finite model theory, we consider a
restricted form of negation, guarded negation. We introduce a fragment of SQL,
called GN-SQL, as well as a fragment of Datalog with stratified negation,
called GN-Datalog, that allow only guarded negation, and we show that these
query languages are computationally well behaved, in terms of testing query
containment, query evaluation, open-world query answering, and boundedness.
GN-SQL and GN-Datalog subsume a number of well known query languages and
constraint languages, such as unions of conjunctive queries, monadic Datalog,
and frontier-guarded tgds. In addition, an analysis of standard benchmark
workloads shows that most usage of negation in SQL in practice is guarded
negation
Rigid Tree Automata and Applications
International audienceWe introduce the class of Rigid Tree Automata (RTA), an extension of standard bottom-up automata on ranked trees with distinguished states called rigid. Rigid states define a restriction on the computation of RTA on trees: RTA can test for equality in subtrees reaching the same rigid state. RTA are able to perform local and global tests of equality between subtrees, non-linear tree pattern matching, and some inequality and disequality tests as well. Properties like determinism, pumping lemma, Boolean closure, and several decision problems are studied in detail. In particular, the emptiness problem is shown decidable in linear time for RTA whereas membership of a given tree to the language of a given RTA is NP-complete. Our main result is the decidability of whether a given tree belongs to the rewrite closure of an RTA language under a restricted family of term rewriting systems, whereas this closure is not an RTA language. 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, in particular for the verification of communicating processes with several local non rewritable memories, like security protocols. Finally, a comparison of RTA with several classes of tree automata with local and global equality tests, with dag automata and Horn clause formalisms is also provided
E-Generalization Using Grammars
We extend the notion of anti-unification to cover equational theories and
present a method based on regular tree grammars to compute a finite
representation of E-generalization sets. We present a framework to combine
Inductive Logic Programming and E-generalization that includes an extension of
Plotkin's lgg theorem to the equational case. We demonstrate the potential
power of E-generalization by three example applications: computation of
suggestions for auxiliary lemmas in equational inductive proofs, computation of
construction laws for given term sequences, and learning of screen editor
command sequences.Comment: 49 pages, 16 figures, author address given in header is meanwhile
outdated, full version of an article in the "Artificial Intelligence
Journal", appeared as technical report in 2003. An open-source C
implementation and some examples are found at the Ancillary file
Primal logic of information
Primal logic arose in access control; it has a remarkably efficient (linear
time) decision procedure for its entailment problem. But primal logic is a
general logic of information. In the realm of arbitrary items of information
(infons), conjunction, disjunction, and implication may seem to correspond
(set-theoretically) to union, intersection, and relative complementation. But,
while infons are closed under union, they are not closed under intersection or
relative complementation.
It turns out that there is a systematic transformation of propositional
intuitionistic calculi to the original (propositional) primal calculi; we call
it Flatting. We extend Flatting to quantifier rules, obtaining arguably the
right quantified primal logic, QPL. The QPL entailment problem is
exponential-time complete, but it is polynomial-time complete in the case, of
importance to applications (at least to access control), where the number of
quantifiers is bounded
Proceedings of Sixth International Workshop on Unification
Swiss National Science Foundation; Austrian Federal Ministry of Science and Research; Deutsche Forschungsgemeinschaft (SFB 314); Christ Church, Oxford; Oxford University Computing Laborator
Saturation-based decision procedures for extensions of the guarded fragment
We apply the framework of Bachmair and Ganzinger for saturation-based theorem proving to derive a range of decision procedures for logical formalisms, starting with a simple terminological language EL, which allows for conjunction and existential restrictions only, and ending with extensions of the guarded fragment with equality, constants, functionality, number restrictions and compositional axioms of form S ◦ T ⊆ H. Our procedures are derived in a uniform way using standard saturation-based calculi enhanced with simplification rules based on the general notion of redundancy. We argue that such decision procedures can be applied for reasoning in expressive description logics, where they have certain advantages over traditionally used tableau procedures, such as optimal worst-case complexity and direct correctness proofs.Wir wenden das Framework von Bachmair und Ganzinger fĂĽr saturierungsbasiertes Theorembeweisen an, um eine Reihe von Entscheidungsverfahren fĂĽr logische Formalismen abzuleiten, angefangen von einer simplen terminologischen Sprache EL, die nur Konjunktionen und existentielle Restriktionen erlaubt, bis zu Erweiterungen des Guarded Fragment mit Gleichheit, Konstanten, Funktionalität, Zahlenrestriktionen und Kompositionsaxiomen der Form S ◦ T ⊆ H. Unsere Verfahren sind einheitlich abgeleitet unter Benutzung herkömmlicher saturierungsbasierter KalkĂĽle, verbessert durch Simplifikationsregeln, die auf dem Konzept der Redundanz basieren. Wir argumentieren, daĂź solche Entscheidungsprozeduren fĂĽr das Beweisen in ausdrucksvollen Beschreibungslogiken angewendet werden können, wo sie gewisse Vorteile gegenĂĽber traditionell benutzten Tableauverfahren besitzen, wie z.B. optimale worst-case Komplexität und direkte Korrektheitsbeweise
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