Search results for "Formal languages"
showing 10 items of 322 documents
On the Class of Languages Recognizable by 1-Way Quantum Finite Automata
2007
It is an open problem to characterize the class of languages recognized by quantum finite automata (QFA). We examine some necessary and some sufficient conditions for a (regular) language to be recognizable by a QFA. For a subclass of regular languages we get a condition which is necessary and sufficient. Also, we prove that the class of languages recognizable by a QFA is not closed under union or any other binary Boolean operation where both arguments are significant.
Quantum Pushdown Automata
2000
Quantum finite automata, as well as quantum pushdown automata were first introduced by C. Moore, J. P. Crutchfield [13]. In this paper we introduce the notion of quantum pushdown automata (QPA) in a non-equivalent way, including unitarity criteria, by using the definition of quantum finite automata of [11]. It is established that the unitarity criteria of QPA are not equivalent to the corresponding unitarity criteria of quantum Turing machines [4]. We show that QPA can recognize every regular language. Finally we present some simple languages recognized by QPA, two of them are not recognizable by deterministic pushdown automata and one seems to be not recognizable by probabilistic pushdown …
One Alternation Can Be More Powerful Than Randomization in Small and Fast Two-Way Finite Automata
2013
We show a family of languages that can be recognized by a family of linear-size alternating one-way finite automata with one alternation but cannot be recognized by any family of polynomial-size bounded-error two-way probabilistic finite automata with the expected runtime bounded by a polynomial. In terms of finite automata complexity theory this means that neither 1Σ2 nor 1Π2 is contained in 2P2.
Artin’s Conjecture and Size of Finite Probabilistic Automata
2008
Size (the number of states) of finite probabilistic automata with an isolated cut-point can be exponentially smaller than the size of any equivalent finite deterministic automaton. The result is presented in two versions. The first version depends on Artin's Conjecture (1927) in Number Theory. The second version does not depend on conjectures but the numerical estimates are worse. In both versions the method of the proof does not allow an explicit description of the languages used. Since our finite probabilistic automata are reversible, these results imply a similar result for quantum finite automata.
The complexity of probabilistic versus deterministic finite automata
1996
We show that there exists probabilistic finite automata with an isolated cutpoint and n states such that the smallest equivalent deterministic finite automaton contains \(\Omega \left( {2^{n\tfrac{{\log \log n}}{{\log n}}} } \right)\) states.
Quantum Finite Automata and Probabilistic Reversible Automata: R-trivial Idempotent Languages
2011
We study the recognition of R-trivial idempotent (R1) languages by various models of "decide-and-halt" quantum finite automata (QFA) and probabilistic reversible automata (DH-PRA). We introduce bistochastic QFA (MM-BQFA), a model which generalizes both Nayak's enhanced QFA and DH-PRA. We apply tools from algebraic automata theory and systems of linear inequalities to give a complete characterization of R1 languages recognized by all these models. We also find that "forbidden constructions" known so far do not include all of the languages that cannot be recognized by measure-many QFA.
Languages Recognizable by Quantum Finite Automata
2006
There are several nonequivalent definitions of quantum finite automata. Nearly all of them recognize only regular languages but not all regular languages. On the other hand, for all these definitions there is a result showing that there is a language l such that the size of the quantum automaton recognizing L is essentially smaller than the size of the minimal deterministic automaton recognizing L. For most of the definitions of quantum finite automata the problem to describe the class of the languages recognizable by the quantum automata is still open. The partial results are surveyed in this paper. Moreover, for the most popular definition of the QFA, the class of languages recognizable b…
Hopcroft’s Algorithm and Cyclic Automata
2008
Minimization of deterministic finite automata is a largely studied problem of the Theory of Automata and Formal Languages. It consists in finding the unique (up to isomorphism) minimal deterministic automaton recognizing a set of words. The first approaches to this topic can be traced back to the 1950’s with the works of Huffman and Moore (cf. [12,15]). Over the years several methods to solve this problem have been proposed but the most efficient algorithm in the worst case was given by Hopcroft in [11]. Such an algorithm computes in O(n log n) the minimal automaton equivalent to a given automaton with n states. The Hopcroft’s algorithm has been widely studied, described and implemented by …
Hopcroft's algorithm and tree-like automata
2011
Minimizing a deterministic finite automata (DFA) is a very important problem in theory of automata and formal languages. Hopcroft's algorithm represents the fastest known solution to the such a problem. In this paper we analyze the behavior of this algorithm on a family binary automata, called tree-like automata, associated to binary labeled trees constructed by words. We prove that all the executions of the algorithm on tree-like automata associated to trees, constructed by standard words, have running time with the same asymptotic growth rate. In particular, we provide a lower and upper bound for the running time of the algorithm expressed in terms of combinatorial properties of the trees…
Postselection Finite Quantum Automata
2010
Postselection for quantum computing devices was introduced by S. Aaronson[2] as an excitingly efficient tool to solve long standing problems of computational complexity related to classical computing devices only. This was a surprising usage of notions of quantum computation. We introduce Aaronson's type postselection in quantum finite automata. There are several nonequivalent definitions of quantumfinite automata. Nearly all of them recognize only regular languages but not all regular languages. We prove that PALINDROMES can be recognized by MM-quantum finite automata with postselection. At first we prove by a direct construction that the complement of this language can be recognized this …