We investigate the average-case state and transition complexity of deterministic and nondeterministic finite automata, when choosing a finite language of given maximum word length n uniformly at random. The case where all words are of equal length is also taken into account. It is shown that almost all deterministic finite automata accepting finite languages over a binary input alphabet have st...

A two-way finite automaton is sweeping if its input head can change direction only on the end-markers. For each n ≥ 2, we exhibit a problem that can be solved by a O(n)-state sweeping LasVegas automaton, but needs 2 states on every sweeping deterministic automaton.

This paper presents a method for the evolution of deterministic finite automata that combines genetic programming and cellular encoding. Programs are evolved that specify actions for the incremental growth of a deterministic finite automata from an initial single-state zygote. The results show that, given a test bed of positive and negative samples, the proposed method is successful at inducing...

The synthesis of stochastic finite-state automata is possible using two kinds of components-deterministic finite-state automata and ergodic signal generators. The starting point in such a synthesis methods is a decomposition of stochastic matrix, its representation as a linear form of simple matrices which belong to the class of transition matrices of deterministic automata. New heuristic crite...

A two-way deterministic finite automaton with r(n) reversals performs ≤ r(n) input head reversals on every n-long input. Let 2D[r(n)] be all families of problems solvable by such automata of polynomial size. We prove that the reversal hierarchy 2D[0] ⊆ 2D[1] ⊆ 2D[2] ⊆ · · · is strict, but 2D[O(1)] = 2D[o(n)]. Moreover, the inner-reversal hierarchy 2D(0) ⊆ 2D(1) ⊆ 2D(2) ⊆ · · · , where now the b...

We give a canonical representation for trim acyclic deterministic finite automata (ADFA) with n states over an alphabet of k symbols. Using this normal form, we present a backtracking algorithm for the exact generation of ADFAs. This algorithm is a non trivial adaptation of the algorithm for the exact generation of minimal acyclic deterministic finite automata (MADFA), presented by Almeida et al..

Minimal deterministic finite automata (dfas) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n logn), where n is the number of states of the input dfa, by [Gawrychowski and Jeż: Hyper-minimisation made efficient. Proc. Mfcs, Lncs 5734, 2009] and [Holzer and Maletti: An n logn algorithm for hyper-minim...

The concept of Deterministic Finite Cover Automata (DFCA) was introduced at WIA ’98, as a more compact representation than Deterministic Finite Automata (DFA) for finite languages. In some cases representing a finite language, Nondeterministic Finite Automata (NFA) may significantly reduce the number of states used. The combined power of the succinctness of the representation of finite language...

We investigate finite deterministic automata in sets with non-homogeneous atoms: integers with successor. As there are uncount-ably many deterministic finite automata in this setting, we restrict our attention to automata with semilinear transition function. The main results is a minimization procedure for semilinear automata. The proof is subtle and refers to decidability of existential Presbu...

An automaton model used for validation and type checking with languages defined using R2G2 [1] is presented. First, tree-shaped data is considered to be handled by the automaton model, then the approach is extended to graph shaped data. The presented approach is based on specialized non-deterministic finite state automata. The specialisation copes with unranked tree shaped data. Graph shaped da...