We study position sampling in a two-way nondeterministic finite automaton (2NFA) to measure information flow between state variables, based on the information-theoretic sampling technique proposed in [20]. We prove that for a 2NFA, the language generated by position sampling is regular. We also show that for a 2NFA, we can effectively find a vector of sampling positions that maximizes informati...

This paper reviews some works on finite automaton one-key cryptosystems and related topics such as autonomous finite automata and Latin arrays. It is well known that shift registers are important sequence generators in stream ciphers. But shift registers are merely a special kind of autonomous finite automata. Finite automata were considered as suitable mathematical models of cryptosystems from...

The aim of the paper is to concoct a novel algorithm for the metamorphosis of parallel regular expressions to ε-free nondeterministic finite automata. For a given parallel regular expression r, let m be the number of symbols that occur in r and let C denote the number of concatenation operators in r. In the worst case, 2m+1 states are required for the construction of the non-deterministic finit...

The problem of describing the dynamics of a conserved energy in a cellular automaton in terms of local movements of “particles” (quanta of that energy) has attracted some people’s attention. The one-dimensional case was already solved by Fukś (2000) and Pivato (2002). For the two-dimensional cellular automata, we show that every (contextfree) conservation law can be expressed in terms of such p...

A coloring of edges of a finite directed graph turns the graph into finite-state automaton. The synchronizing word of a deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph of uniform outdegree (constant outdegree of any vertex) is synchronizing if the coloring turns th...

In the 1980’s Stallings [35] showed that every finitely generated subgroup of a free group is canonically represented by a finite minimal immersion of a bouquet of circles. In terms of the theory of automata, this is a minimal finite inverse automaton. This allows for the deep algorithmic theory of finite automata and finite inverse monoids to be used to answer questions about finitely generate...

The synchronization delay of an N-state local automaton is known to be O(N 2). It has been conjectured by S. Kim, R. McNaughton and R. McCloskey that, for deterministic local automata, it is O(N 1:5) on a two-letter alphabet and no less than O(N 2) in the general case. We prove that this conjecture is false and that the synchronization delay is (N 2) in all cases.

We examine the conjecture that no polynomial can upper bound the increase in the number of states when a one-way nondeterministic finite automaton (1nfa) is converted into an equivalent two-way deterministic finite automaton (2dfa). We study the problem of liveness, which admits 1nfas of polynomial size and is known to defy 2dfas of polynomial size if and only if the conjecture is true. We focu...

DEFINITION. A de termin i s t i c l inear bounded a u t o m a t o n (DLBA) is a sixtuple (Q, q0, V, # 1 , # 2 , J ) where: Q is a finite set of states q o , q l .... ; q o E Q is the initial state; V is a finite vocabulary; # 1 , #2 6 V are left and right endmarkers, respectively; and J is a finite set of instructions. T h e automaton consists of two pushdown lists, called L and R, and a finite...

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 versi...