Parallel context-free languages

Efficient Parallel Recognition of Context-Free Languages

This paper presents an efficient parallel approach for recognition of context-free languages. The algorithm takes O(log n) time of computations on a fixed configuration of processors array with reconfigurable bus system. The number of processors required is O(n3). Processor architecture consists of multibus and multiple internal switches in the processors. A specific arrangement of processors i...

Efficient parallel and incremental parsing of practical context-free languages

We present a divide-and-conquer algorithm for parsing context-free languages efficiently. Our algorithm is an instance of Valiant’s (1975), who reduced the problem of parsing to matrix multiplications. We show that, while the conquer step of Valiant’s is O(n), it improves to O(log n) under certain conditions satisfied by many useful inputs, and if one uses a sparse representation of matrices. T...

Context - Free Languages and

Context-Free Languages, Coalgebraically

We give a coalgebraic account of context-free languages using the functor D(X) = 2 × X for deterministic automata over an alphabet A, in three different but equivalent ways: (i) by viewing context-free grammars as D-coalgebras; (ii) by defining a format for behavioural differential equations (w.r.t. D) for which the unique solutions are precisely the context-free languages; and (iii) as theD-co...

Context-Free Languages

Introduction 1 1 Languages 3 1.1 Notation and examples . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 Grammars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Ambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Reduced grammars, normal forms . . . . . . . . . . . . . . . 6 1.1...