Search results for "DFA"
showing 10 items of 54 documents
Transition Function Complexity of Finite Automata
2011
State complexity of finite automata in some cases gives the same complexity value for automata which intuitively seem to have completely different complexities. In this paper we consider a new measure of descriptional complexity of finite automata -- BC-complexity. Comparison of it with the state complexity is carried out here as well as some interesting minimization properties are discussed. It is shown that minimization of the number of states can lead to a superpolynomial increase of BC-complexity.
The Complexity of Probabilistic versus Quantum Finite Automata
2002
We present a language Ln which is recognizable by a probabilistic finite automaton (PFA) with probability 1 - ? for all ? > 0 with O(log2 n) states, with a deterministic finite automaton (DFA) with O(n) states, but a quantum finite automaton (QFA) needs at least 2?(n/log n) states.
Non-constructive Methods for Finite Probabilistic Automata
2007
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.
NON-CONSTRUCTIVE METHODS FOR 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. However, the proof is non-constructive. 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 not proved 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.
On extremal cases of Hopcroft’s algorithm
2010
AbstractIn this paper we consider the problem of minimization of deterministic finite automata (DFA) with reference to Hopcroft’s algorithm. Hopcroft’s algorithm has several degrees of freedom, so there can exist different executions that can lead to different sequences of refinements of the set of the states up to the final partition. We find an infinite family of binary automata for which such a process is unique, whatever strategy is chosen. Some recent papers (cf. Berstel and Carton (2004) [3], Castiglione et al. (2008) [6] and Berstel et al. (2009) [1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata as…
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.
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 …