Reversible Top-Down Syntax Analysis

Abstract

Top-down syntax analysis can be based on [Formula: see text] grammars. The canonical acceptors for [Formula: see text] languages are deterministic stateless pushdown automata with input lookahead of size [Formula: see text]. We investigate the computational capacity of reversible computations of such automata. A pushdown automaton with lookahead [Formula: see text] is said to be reversible if its predecessor configurations can uniquely be computed by a pushdown automaton with backward input lookahead (lookback) of size [Formula: see text]. It is shown that we cannot trade a lookahead for states or vice versa. The impact of having states or a lookahead depends on the language. While reversible pushdown automata with states accept all regular languages, we are going to prove that there are regular languages that cannot be accepted reversibly without states, even in case of an arbitrarily large lookahead. This completes the comparison of reversible with ordinary pushdown automata in our setting. Moreover, it turns out that there are problems which can be solved by reversible deterministic stateless pushdown automata with lookahead of size [Formula: see text], but not by any reversible deterministic stateless pushdown automaton with lookahead of size [Formula: see text]. So, an infinite and tight hierarchy of language families dependent on the size of the lookahead is shown. Finally, we prove that the language families accepted by reversible deterministic stateless pushdown automata with lookahead of size [Formula: see text] are not closed under standard operations. For example, we show that the families are anti-AFLs which are not closed under intersection.