155 research outputs found
Syntactic Complexity of R- and J-Trivial Regular Languages
The syntactic complexity of a regular language is the cardinality of its
syntactic semigroup. The syntactic complexity of a subclass of the class of
regular languages is the maximal syntactic complexity of languages in that
class, taken as a function of the state complexity n of these languages. We
study the syntactic complexity of R- and J-trivial regular languages, and prove
that n! and floor of [e(n-1)!] are tight upper bounds for these languages,
respectively. We also prove that 2^{n-1} is the tight upper bound on the state
complexity of reversal of J-trivial regular languages.Comment: 17 pages, 5 figures, 1 tabl
Representability of nonregular languages in finite probabilistic automata
In this paper the necessary and sufficient conditions of representability of nonregular languages in finite probabilistic automata are formulated
Universal computation and other capabilities of hybrid and continuous dynamical systems
Caption title.Includes bibliographical references (p. 25-27).Supported by the Army Research Office and the Center for Intelligent Control Systems. DAAL03-92-G-0164 DAAL03-92-G-0115Michael S. Branicky
Non-Deterministic Communication Complexity of Regular Languages
In this thesis, we study the place of regular languages within the
communication complexity setting. In particular, we are interested in the
non-deterministic communication complexity of regular languages.
We show that a regular language has either O(1) or Omega(log n)
non-deterministic complexity. We obtain several linear lower bound results
which cover a wide range of regular languages having linear non-deterministic
complexity. These lower bound results also imply a result in semigroup theory:
we obtain sufficient conditions for not being in the positive variety Pol(Com).
To obtain our results, we use algebraic techniques. In the study of regular
languages, the algebraic point of view pioneered by Eilenberg (\cite{Eil74})
has led to many interesting results. Viewing a semigroup as a computational
device that recognizes languages has proven to be prolific from both semigroup
theory and formal languages perspectives. In this thesis, we provide further
instances of such mutualism.Comment: Master's thesis, 93 page
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