Finite State Automaton Group
K. Thiagarajan, S. Jeya Bharathi, A. Jeyanthi, J. Padmashree · 2013
This paper deals with the Group structure of Finite State Machine when δ is total. Also we defined the sub FSM group, Normal FSM group and the partially ordered FSM group. Finite state Machine may be taken into account for the transfer of topological structure in different way, to intend different applications of finite automata to group Theory, mentioning also some generalizations to the wider context of monoids. REVIOUS algebraic investigations of Finite-State Machines (FSM) have made use of a semi group structure defined on finite strings of elements taken from the input set of the machine. Representations for the machines(1) are then given in terms of certain homomorphic mappings of these input strings(2).We give the group structure for the finite state machines in a complete FSM.(ie) when δ is total. In the present paper, we give an algebraic proof of this property of finite J-trivial FSM (3) Groups. Our argument which is based on the ideal (4) structure of finite J- trivial FSM Group.The connections to the finite groups being obvious and well known. Most of course will be focused on free groups and close structures, but also discuss some applications to wider classes of high geometric significance such as hyperbolic groups, automatic groups and self-similar groups