Symbolic Lookaheads for Bottom-up Parsing

We present algorithms for the construction of LALR(1) parsing tables, and of LR(1) parsing tables of reduced size. We first define specialized characteristic automata whose states are parametric w.r.t. variables symbolically representing lookahead-sets. The propagation flow of lookaheads is kept in the form of a system of recursive equations, which is resolved to obtain the concrete LALR(1) table. By inspection of the LALR(1) automaton and of its lookahead propagation flow, we decide whether the grammar is LR(1) or not. In the positive case, an LR(1) parsing table of reduced size is computed by refinement of the LALR(1) table.

We present algorithms for the construction of LALR(1) parsing tables, and of LR(1) parsing tables of reduced size. We first define specialized characteristic automata whose states are parametric w.r.t. variables symbolically representing lookahead-sets. The propagation flow of lookaheads is kept in the form of a system of recursive equations, which is resolved to obtain the concrete LALR(1) table. By inspection of the LALR(1) automaton and of its lookahead ropagation flow, we decide whether the grammar is LR(1) or not. In the positive case, an LR(1) parsing table of reduced size is computed by refinement of the LALR(1) table.