finite state machine

The Automata Interpretation of Integer Sequences

Authors: Epifanov A. S.

Transformation of phase pictures to geometrical images of laws of functioning of state machines, offered and developed by V.A.Tverdokhlebov , has allowed to represent phase pictures by uniform mathematical structures –- broken lines with numerical coordinates of points. V.A.Tverdokhlebov shows, that sequence of elements from the finite set, combined with linear order on set of input words, defines laws of functioning of the discrete determined dynamic system (state machine).

The Algorithm for Checking Transitivity of Mappings Associated with the Finite State Machines from the Groups ASp

Authors: Karandashov M. V.

The paper deals with a question of determining the property of transitivity for mappings defined by finite automata. A criterion of transitivity for mappings defined by finite automata on the words of finite length in terms of finite automata and trees of deterministic functions is presented. It is shown that for finite automata from groups ASp an algorithm can be constructed for checking transitivity. To prove this fact some properties of Abelian groups of permutations are used.