PUSHDOWN AUTOMATA WITH BOUNDED BACKTRACK

Abstract

Abstract : The report considers two classes of pushdown automata (pda), and the languages accepted by them. These pda accept their languages rapidly because they reread the input word a limited number of times, hence, such languages are particularly useful as programming languages. The first class, strong bounded backtrack pda, read input words from left to right, and jump from right to left (backtrack). The languages accepted by such automata will be shown to be equivalent to the finite unions of deterministic languages. The second class, weak bounded backtrack an arbitrary number of times. The device reads a word from left to right, simulating the action of the pda. Every time the pda reaches a total configuration (state and pushdown tape) in which it is possible to read another input letter, that configuration is stored. If no move at all is possible in a given configuration, it is erased from storage. Thus one can accept the language with no backtrack without having to keep track of an arbitrary number of possible configurations of the pda. Several results will be shown about each of these classes of pda, including operations that preserve the properties. While these properties are not preserved by all gsm mappings, it will be shown that information lossless gsm's preserve the weak bounded backtrack property, and information lossless gsm's of finite order preserve the strong bounded backtrack property.