327 research outputs found
Finitary languages
The class of omega-regular languages provides a robust specification language
in verification. Every omega-regular condition can be decomposed into a safety
part and a liveness part. The liveness part ensures that something good happens
"eventually". Finitary liveness was proposed by Alur and Henzinger as a
stronger formulation of liveness. It requires that there exists an unknown,
fixed bound b such that something good happens within b transitions. In this
work we consider automata with finitary acceptance conditions defined by
finitary Buchi, parity and Streett languages. We study languages expressible by
such automata: we give their topological complexity and present a
regular-expression characterization. We compare the expressive power of
finitary automata and give optimal algorithms for classical decisions
questions. We show that the finitary languages are Sigma 2-complete; we present
a complete picture of the expressive power of various classes of automata with
finitary and infinitary acceptance conditions; we show that the languages
defined by finitary parity automata exactly characterize the star-free fragment
of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete
and universality as well as language inclusion are PSPACE-complete for finitary
parity and Streett automata
IST Austria Technical Report
The class of Ï regular languages provide a robust specification language in verification. Every Ï-regular condition can be decomposed into a safety part and a liveness part. The liveness part ensures that something good happens âeventually.â Two main strengths of the classical, infinite-limit formulation of liveness are robustness (independence from the granularity of transitions) and simplicity (abstraction of complicated time bounds). However, the classical liveness formulation suffers from the drawback that the time until something good happens may be unbounded. A stronger formulation of liveness, so-called finitary liveness, overcomes this drawback, while still retaining robustness and simplicity. Finitary liveness requires that there exists an unknown, fixed bound b such that something good happens within b transitions. In this work we consider the finitary parity and Streett (fairness) conditions. We present the topological, automata-theoretic and logical characterization of finitary languages defined by finitary parity and Streett conditions. We (a) show that the finitary parity and Streett languages are ÎŁ2-complete; (b) present a complete characterization of the expressive power of various classes of automata with finitary and infinitary conditions (in particular we show that non-deterministic finitary parity and Streett automata cannot be determinized to deterministic finitary parity or Streett automata); and (c) show that the languages defined by non-deterministic finitary parity automata exactly characterize the star-free fragment of ÏB-regular languages
Algebraic recognizability of regular tree languages
We propose a new algebraic framework to discuss and classify recognizable
tree languages, and to characterize interesting classes of such languages. Our
algebraic tool, called preclones, encompasses the classical notion of syntactic
Sigma-algebra or minimal tree automaton, but adds new expressivity to it. The
main result in this paper is a variety theorem \`{a} la Eilenberg, but we also
discuss important examples of logically defined classes of recognizable tree
languages, whose characterization and decidability was established in recent
papers (by Benedikt and S\'{e}goufin, and by Bojanczyk and Walukiewicz) and can
be naturally formulated in terms of pseudovarieties of preclones. Finally, this
paper constitutes the foundation for another paper by the same authors, where
first-order definable tree languages receive an algebraic characterization
IST Austria Technical Report
We consider two-player games played on graphs with request-response and finitary Streett objectives. We show these games are PSPACE-hard, improving the previous known NP-hardness. We also improve the lower bounds on memory required by the winning strategies for the players
A Unifying Splitting Framework
International audienceAVATAR is an elegant and effective way to split clauses in a saturation prover using a SAT solver. But is it refutationally complete? And how does it relate to other splitting architectures? To answer these questions, we present a unifying framework that extends a saturation calculus (e.g., superposition) with splitting and embeds the result in a prover guided by a SAT solver. The framework also allows us to study locking, a subsumption-like mechanism based on the current propositional model. Various architectures are instances of the framework, including AVATAR, labeled splitting, and SMT with quantifiers
Intensional and Extensional Semantics of Bounded and Unbounded Nondeterminism
We give extensional and intensional characterizations of nondeterministic
functional programs: as structure preserving functions between biorders, and as
nondeterministic sequential algorithms on ordered concrete data structures
which compute them. A fundamental result establishes that the extensional and
intensional representations of non-deterministic programs are equivalent, by
showing how to construct a unique sequential algorithm which computes a given
monotone and stable function, and describing the conditions on sequential
algorithms which correspond to continuity with respect to each order.
We illustrate by defining may and must-testing denotational semantics for a
sequential functional language with bounded and unbounded choice operators. We
prove that these are computationally adequate, despite the non-continuity of
the must-testing semantics of unbounded nondeterminism. In the bounded case, we
prove that our continuous models are fully abstract with respect to may and
must-testing by identifying a simple universal type, which may also form the
basis for models of the untyped lambda-calculus. In the unbounded case we
observe that our model contains computable functions which are not denoted by
terms, by identifying a further "weak continuity" property of the definable
elements, and use this to establish that it is not fully abstract
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