Reversible Top-Down Syntax Analysis

Abstract

Top-down syntax analysis can be based on $\mathrm {LL}(k)$ grammars. The canonical acceptors for $\mathrm {LL}(k)$ languages are deterministic stateless pushdown automata with input lookahead of size k. We investigate the computational capacity of reversible computations of such automata. A pushdown automaton with lookahead k is said to be reversible if its predecessor configurations can uniquely be computed by a pushdown automaton with backward input lookahead (lookback) of size k. 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. Finally, it turns out that there are problems which can be solved by reversible deterministic stateless pushdown automata with lookahead of size $k+1$, but not by any reversible deterministic stateless pushdown automaton with lookahead of size k. So, an infinite and tight hierarchy of language families dependent on the size of the lookahead is shown.