Deterministic Input-Reversal and Input-Revolving Finite Automata

Extended finite automata are finite state machines with the additional ability to manipulate the remaining part of the input. We investigate three types of deterministic extended automata, namely left-revolving, right-revolving, and input reversal finite automata. Concerning their computational capacity it is shown that nondeterminism is better than determinism, that is, for all three types of automata there is a language accepted by the nondeterministic versions but not accepted by any deterministic automaton of the same type. Concerning the closure properties most of the language families studied are not closed under standard operations. In particular, we show that the family of languages accepted by deterministic right-revolving finite automata is an anti-AFL which is not closed under reversal and intersection.

[1]  Christopher Culy,et al.  Formal properties of natural language and linguistic theories , 1996 .

[2]  Seymour Ginsburg,et al.  Algebraic and Automata Theoretic Properties of Formal Languages , 1975 .

[3]  Martin Kutrib,et al.  Input Reversals and Iterated Pushdown Automata: A New Characterization of Khabbaz Geometric Hierarchy of Languages , 2004, Developments in Language Theory.

[4]  Palash Sarkar.  Pushdown Automaton with the Ability to Flip its Stack , 2001, Electron. Colloquium Comput. Complex..

[5]  Martin Kutrib,et al.  Revolving-Input Finite Automata , 2005, Developments in Language Theory.

[6]  Dana S. Scott,et al.  Finite Automata and Their Decision Problems , 1959, IBM J. Res. Dev..

[7]  Martin Kutrib,et al.  Flip-Pushdown Automata: Nondeterminism Is Better than Determinism , 2003, Developments in Language Theory.

[8]  Robin Milner,et al.  On Observing Nondeterminism and Concurrency , 1980, ICALP.

[9]  Samuel Eilenberg,et al.  Review of "Algebraic and automata-theoretic properties of formal languages" by Seymour Ginsburg. North Holland, 1975. , 1976, SIGA.

[10]  Martin Kutrib,et al.  Hybrid Extended Finite Automata , 2006, CIAA.

[11]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

[12]  Martin Kutrib,et al.  Flip-Pushdown Automata: k+1 Pushdown Reversals Are Better than k , 2003, ICALP.

[13]  Borivoj Melichar,et al.  Finding Common Motifs with Gaps Using Finite Automata , 2006, CIAA.

[14]  Grzegorz Rozenberg,et al.  Developments in Language Theory II , 2002 .

[15]  Seymour Ginsburg,et al.  One-way stack automata , 1967, JACM.