An efficient context-free parsing algorithm
Communications of the ACM
Petri Nets and Grafcet: Tools for Modelling Discrete Event Systems
Petri Nets and Grafcet: Tools for Modelling Discrete Event Systems
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Regulated Rewriting in Formal Language Theory
Regulated Rewriting in Formal Language Theory
The theory of parsing, translation, and compiling
The theory of parsing, translation, and compiling
Petri Net Control for Grammar Systems
Formal and Natural Computing - Essays Dedicated to Grzegorz Rozenberg [on occasion of his 60th birthday, March 14, 2002]
k-Petri Net Controlled Grammars
Language and Automata Theory and Applications
Erasing in Petri Net Languages and Matrix Grammars
DLT '09 Proceedings of the 13th International Conference on Developments in Language Theory
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In this paper we introduce an algorithm which solves the membership problem of Petri net controlled grammars without @l-rules and cyclic rules. We define a conditional tree which is a modified derivation tree of a context-free grammar with information about control by a Petri net. It is shown that a conditional tree is cancelled to a derivation tree without conditions if and only if there is a derivation under the control of the Petri net from the start symbol to a word which is the yielding of the conditional tree. Then the Earley's algorithm is extended to make a conditional tree in addition to parse a word. Thus the word is generated by a given Petri net controlled grammar if and only if the resulting conditional tree is cancelled to a tree of no condition. The time complexity of the algorithm is nondeterministic polynomial of the length of an input word. Therefore the class of languages generated by Petri net controlled grammars without @l-rules and cyclic rules is included in the class of context-sensitive languages.