35,357 research outputs found
A Rice-style theorem for parallel automata
AbstractWe present a general result, similar to Rice’s theorem, concerning the complexity of detecting properties on finite automata enriched by bounded cooperative concurrency, such as statecharts and abstract parallel automata, which we denote by CFAs (Concurrent Finite Automata). On one extreme, the complexity of detecting non-trivial properties that preserve equivalence of machines, i.e. properties of the accepted language, on finite automata, can be as little as O(1). On the other extreme, Rice’s theorem states that all such properties on Turing machines are undecidable. We state that all the non-trivial properties of the regular (or ω-regular) languages, are PSPACE-hard on CFAs with ϵ-moves and on CFAs without ϵ-moves accepting infinite words. We also extend this result to CFAs without ϵ-moves accepting finite words that satisfy a condition that holds for many properties
Power of Randomization in Automata on Infinite Strings
Probabilistic B\"uchi Automata (PBA) are randomized, finite state automata
that process input strings of infinite length. Based on the threshold chosen
for the acceptance probability, different classes of languages can be defined.
In this paper, we present a number of results that clarify the power of such
machines and properties of the languages they define. The broad themes we focus
on are as follows. We present results on the decidability and precise
complexity of the emptiness, universality and language containment problems for
such machines, thus answering questions central to the use of these models in
formal verification. Next, we characterize the languages recognized by PBAs
topologically, demonstrating that though general PBAs can recognize languages
that are not regular, topologically the languages are as simple as
\omega-regular languages. Finally, we introduce Hierarchical PBAs, which are
syntactically restricted forms of PBAs that are tractable and capture exactly
the class of \omega-regular languages
Contributions to the Theory of Finite-State Based Grammars
This dissertation is a theoretical study of finite-state based grammars used in natural language processing. The study is concerned with certain varieties of finite-state intersection grammars (FSIG) whose parsers define regular relations between surface strings and annotated surface strings. The study focuses on the following three aspects of FSIGs:
(i) Computational complexity of grammars under limiting parameters In the study, the computational complexity in practical natural language processing is approached through performance-motivated parameters on structural complexity. Each parameter splits some grammars in the Chomsky hierarchy into an infinite set of subset approximations. When the approximations are regular, they seem to fall into the logarithmic-time hierarchyand the dot-depth hierarchy of star-free regular languages. This theoretical result is important and possibly relevant to grammar induction.
(ii) Linguistically applicable structural representations Related to the linguistically applicable representations of syntactic entities, the study contains new bracketing schemes that cope with dependency links, left- and right branching, crossing dependencies and spurious ambiguity. New grammar representations that resemble the Chomsky-Schützenberger representation of context-free languages are presented in the study, and they include, in particular, representations for mildly context-sensitive non-projective dependency grammars whose performance-motivated approximations are linear time parseable.
(iii) Compilation and simplification of linguistic constraints Efficient compilation methods for certain regular operations such as generalized restriction are presented. These include an elegant algorithm that has already been adopted as the approach in a proprietary finite-state tool. In addition to the compilation methods, an approach to on-the-fly simplifications of finite-state representations for parse forests is sketched.
These findings are tightly coupled with each other under the theme of locality. I argue that the findings help us to develop better, linguistically oriented formalisms for finite-state parsing and to develop more efficient parsers for natural language processing.
Avainsanat: syntactic parsing, finite-state automata, dependency grammar, first-order logic, linguistic performance, star-free regular approximations, mildly context-sensitive grammar
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
An Upper Bound on the Complexity of Recognizable Tree Languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular
tree language of infinite trees is in a class
for some natural number , where is the game quantifier. We
first give a detailed exposition of this result. Next, using an embedding of
the Wadge hierarchy of non self-dual Borel subsets of the Cantor space
into the class , and the notions of Wadge degree
and Veblen function, we argue that this upper bound on the topological
complexity of regular tree languages is much better than the usual
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