5,455 research outputs found
Regular and context-free pattern languages over small alphabets
Pattern languages are generalisations of the copy language, which is a standard
textbook example of a context-sensitive and non-context-free language. In this
work, we investigate a counter-intuitive phenomenon: with respect to alphabets
of size 2 and 3, pattern languages can be regular or context-free in an unexpected
way. For this regularity and context-freeness of pattern languages, we give
several sufficient and necessary conditions and improve known results
Regular and context-free pattern languages over small alphabets
Pattern languages are generalisations of the copy language,
which is a standard textbook example of a context-sensitive and noncontext-
free language. In this work, we investigate a counter-intuitive
phenomenon: with respect to alphabets of size 2 and 3, pattern languages
can be regular or context-free in an unexpected way. For this regularity
and context-freeness of pattern languages, we give several sufficient and
necessary conditions and improve known results
Regular and Context-Free Pattern Languages over Small Alphabets
Pattern languages are generalisations of the copy language, which is a standard
textbook example of a context-sensitive and non-context-free language. In this
work, we investigate a counter-intuitive phenomenon: with respect to alphabets
of size 2 and 3, pattern languages can be regular or context-free in an unexpected
way. For this regularity and context-freeness of pattern languages, we give
several sufficient and necessary conditions and improve known results
Digraph Complexity Measures and Applications in Formal Language Theory
We investigate structural complexity measures on digraphs, in particular the
cycle rank. This concept is intimately related to a classical topic in formal
language theory, namely the star height of regular languages. We explore this
connection, and obtain several new algorithmic insights regarding both cycle
rank and star height. Among other results, we show that computing the cycle
rank is NP-complete, even for sparse digraphs of maximum outdegree 2.
Notwithstanding, we provide both a polynomial-time approximation algorithm and
an exponential-time exact algorithm for this problem. The former algorithm
yields an O((log n)^(3/2))- approximation in polynomial time, whereas the
latter yields the optimum solution, and runs in time and space O*(1.9129^n) on
digraphs of maximum outdegree at most two. Regarding the star height problem,
we identify a subclass of the regular languages for which we can precisely
determine the computational complexity of the star height problem. Namely, the
star height problem for bideterministic languages is NP-complete, and this
holds already for binary alphabets. Then we translate the algorithmic results
concerning cycle rank to the bideterministic star height problem, thus giving a
polynomial-time approximation as well as a reasonably fast exact exponential
algorithm for bideterministic star height.Comment: 19 pages, 1 figur
The separation problem for regular languages by piecewise testable languages
Separation is a classical problem in mathematics and computer science. It
asks whether, given two sets belonging to some class, it is possible to
separate them by another set of a smaller class. We present and discuss the
separation problem for regular languages. We then give a direct polynomial time
algorithm to check whether two given regular languages are separable by a
piecewise testable language, that is, whether a sentence can
witness that the languages are indeed disjoint. The proof is a reformulation
and a refinement of an algebraic argument already given by Almeida and the
second author
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
Speech Recognition by Composition of Weighted Finite Automata
We present a general framework based on weighted finite automata and weighted
finite-state transducers for describing and implementing speech recognizers.
The framework allows us to represent uniformly the information sources and data
structures used in recognition, including context-dependent units,
pronunciation dictionaries, language models and lattices. Furthermore, general
but efficient algorithms can used for combining information sources in actual
recognizers and for optimizing their application. In particular, a single
composition algorithm is used both to combine in advance information sources
such as language models and dictionaries, and to combine acoustic observations
and information sources dynamically during recognition.Comment: 24 pages, uses psfig.st
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