We provide a new construction of a nondeterministic finite automaton (NFA) accepting the pushdown store language of a given pushdown automaton (PDA). The resulting NFA has a number of states which is quadratic in the number of states and linear in the number of pushdown symbols of the given PDA. Moreover, we prove the size optimality of our construction. Beside improving some results in the lit...

We investigate the mean dimension of a cellular automaton (CA for short) with compact non-discrete space states. A formula is established (near) strongly permutative, permutative algebraic and unit one-dimensional automata. In higher dimensions, CA or having spaceship has infinite dimension. However, building on Meyerovitch’s example [Mey08], we give an surjective positive finite

Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because information requires physical representations and because many natural processes have been recognized to complete in non-deterministic polynomial time ( ). The irreversible process with three or more d...

In this paper, first a simplified version of a general fuzzy automaton with a fixed c is defined and then a subepisode of a simplified version of a general fuzzy automaton with a constant c is defined and explained connected and strong connected them, and finally, a model of quasi-order hypergroup on general fuzzy automaton with constant c is presented and the relationships between them are rev...

The complementation problem for nondeterministic word automata has numerous applications in formal verification. In order to check that the language of an automaton A1 is contained in the language of a second automaton A2, one checks that the intersection of A1 with an automaton that complements A2 is empty. Many problems in verification and design are reduced to language containment. In model ...

• F ⊆ Q is the set of accept or final states. The behavior of a DFA M on an input string x ∈ Σ∗ is as follows. It reads the symbols in x one at a time, from left to right. At each point in time, the automaton has a current state. Initially, the automaton is in state s. If the current state of the automaton is q, and the next symbol in x to be read is a, then the automaton on reading a transitio...

The problem of transforming a lattice into a non-deterministic finite state automaton is non-trivial. We present a transformation algorithm which tracks, for each node of an automaton under construction, the larcs which it reflects and the lattice nodes at their origins and extremities. An extension of the algorithm permits the inclusion of null, or epsilon, arcs in the output automaton. The al...

This paper addresses first and foremost the following issue: given a finite alphabet A, a set of words X ⊂ A, and a word u ∈ A, we want to efficiently determine whether u ∈ X. With a nondeterministic automaton, one can determine whether a word u is in X in time proportional to the product of the lengths of u and X , where the length of X is defined as the sum of the lengths of its elements. Wit...

An elementary cellular automaton with memory is a chain of finite state machines (cells) updating their state simultaneously and by the same rule. Each cell updates its current state depending on current states of its immediate neighbours and a certain number of its own past states. Some cellstate transition rules support gliders, compact patterns of non-quiescent states translating along the c...