Search results for "Formal language"
showing 10 items of 357 documents
Group Input Machine
2009
We introduce a new type of internal memory for finite automata and real-time automata. Instead of using tapes with a prescribed Euclidean structure (one-dimensional or two-dimensional tapes) we allow arbitrary group structure of the internal memory of the automata.
Extremal minimality conditions on automata
2012
AbstractIn this paper we investigate the minimality problem of DFAs by varying the set of final states. In other words, we are interested on how the choice of the final states can affect the minimality of the automata. The state-pair graph is a useful tool to investigate such a problem. The choice of a set of final states for the automaton A defines a coloring of the closed components of the state-pair graph and the minimality of A corresponds to a property of these colored components. A particular attention is devoted to the analysis of some extremal cases such as, for example, the automata that are minimal for any choice of the subset of final states F from the state set Q of the automato…
Automata with Extremal Minimality Conditions
2010
It is well known that the minimality of a deterministic finite automaton (DFA) depends on the set of final states. In this paper we study the minimality of a strongly connected DFA by varying the set of final states. We consider, in particular, some extremal cases. A strongly connected DFA is called uniformly minimal if it is minimal, for any choice of the set of final states. It is called never-minimal if it is not minimal, for any choice of the set of final states. We show that there exists an infinite family of uniformly minimal automata and that there exists an infinite family of never-minimal automata. Some properties of these automata are investigated and, in particular, we consider t…
A graph theoretic approach to automata minimality
2012
AbstractThe paper presents a graph-theoretic approach to test the minimality of a deterministic automaton. In particular, we focus on problems concerning the dependence of the minimality of an automaton on the choice of the set F of final states or on the cardinality of the set F. We introduce different minimality conditions of an automaton and show that such conditions can be characterized in graph-theoretic terms.
Nondeterministic Moore Automata and Brzozowski’s Algorithm
2011
Moore automata represent a model that has many applications. In this paper we define a notion of coherent nondeterministic Moore automaton (NMA) and show that such a model has the same computational power of the classical deterministic Moore automaton. We consider also the problem of constructing the minimal deterministic Moore automaton equivalent to a given NMA. In this paper we propose an algorithm that is a variant of Brzozowski's algorithm in the sense that it is essentially structured as reverse operation and subset construction performed twice.
On Extremal Cases of Hopcroft’s Algorithm
2009
In 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 sequences of refinements of the set of the states that lead to the final partition. We find an infinite family of binary automata for which such a process is unique. Some recent papers (cf. [3,7,1]) have been devoted to find families of automata for which Hopcroft’s algorithm has its worst execution time. They are unary automata associated to circular words. However, automata minimization can be achieved also in linear time when the alphabet has only one letter (cf. [14]), so in …
Minimal nontrivial space complexity of probabilistic one- way turing machines
2005
Languages recognizable in o(log log n) space by probabilistic one — way Turing machines are proved to be regular. This solves an open problem in [4].
The monadic quantifier alternation hierarchy over grids and pictures
1998
The subject of this paper is the expressive power of monadic second-order logic over two-dimensional grids. We give a new, self-contained game-theoretical proof of the nonexpressibility results of Matz and Thomas. As we show, this implies the strictness of the monadic second-order quantifier alternation hierarchy over grids.
Size of Quantum Finite State Transducers
2007
Sizes of quantum and deterministic finite state transducers are compared in the case when both quantum and deterministic finite state transducers exist. The difference in size may be exponential.
On Finite Satisfiability of the Guarded Fragment with Equivalence or Transitive Guards
2007
The guarded fragment of first-order logic, GF, enjoys the finite model property, so the satisfiability and the finite satisfiability problems coincide. We are concerned with two extensions of the two-variable guarded fragment that do not possess the finite model property, namely, GF2 with equivalence and GF2 with transitive guards. We prove that in both cases every finitely satisfiable formula has a model of at most double exponential size w.r.t. its length. To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2NEXPTIME-upper bound on the complexity of the fini…