Huynh, D.T.: "Commutative Grammars: The Complexity of Uniform Word Problems", Information and Control 57, 1983, 21--39.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....nets are also called communication free nets [6] What makes BPP nets theoretically interesting, aside from their close connection to BPPs, includes the following. First, BPP nets are also computationally equivalent to the so called commutative context free grammars defined and investigated in [10,11]. Of many problems considered in [10] the uniform word problem was shown to be solvable in NP through a somewhat compli cated proof. In a recent article [4] an alternative and simpler proof has been Preprint submitted to Elsevier Science 27 January given for the NP upper bound of the uniform ....

....nets [6] What makes BPP nets theoretically interesting, aside from their close connection to BPPs, includes the following. First, BPP nets are also computationally equivalent to the so called commutative context free grammars defined and investigated in [10,11] Of many problems considered in [10], the uniform word problem was shown to be solvable in NP through a somewhat compli cated proof. In a recent article [4] an alternative and simpler proof has been Preprint submitted to Elsevier Science 27 January given for the NP upper bound of the uniform word problem, taking advantage of the ....

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D. Huynh, Commutative grammars: the complexity of uniform word problems, Inform. and Comput. 57 (1983) 21-39.

.... PSPACE complete for nets in which every transition has the same number of input and output places [44] ffl NP complete for Petri nets without cycles [68] ffl NP complete for sinkless and normal Petri nets [36] ffl NP complete for conflict free Petri nets [31] ffl NP complete for BPP nets [38, 19]; ffl polynomial for bounded conflict free Petri nets [31] In [7] these nets are called reversible. 7 ffl polynomial for marked graphs [13, 15] a Petri net is a marked graph if every place has exactly one input transition and one output transition (notice that marked graphs are ....

D.T. Huynh. Commutative Grammars: The Complexity of Uniform Word Problems. Information and Control 57, 21--39 (1983).

....Process. This is a class of CCS processes defined by Christensen [11] see also the Concurrency column of the EATCS Bulletin 51) BPPs can be given a net semantics in terms of BPP nets. BPP nets are also computationally equivalent to commutative context free grammars, as defined by Huynh in [39]. ffl free choice if, whenever an arc connects a place s to a transition t, either t is the unique output transition of s, or s is the unique input place of t. ffl 1 safe if, for every place s and every reachable marking M , M(s) 1; i.e. no reachable marking ever puts more than one token in ....

.... for 1 safe Petri nets [10] ffl PSPACE complete for single path Petri nets [31] ffl NP complete for Petri nets without cycles [74] ffl NP complete for sinkless and normal Petri nets [37] ffl NP complete for conflict free Petri nets [32] ffl NP complete for BPP nets [39, 20]; ffl polynomial for bounded conflict free Petri nets [32] ffl polynomial for marked graphs [14, 16] a Petri net is a marked graph if every place has exactly one input transition and one output transition (notice that marked graphs are conflict free) ffl polynomial for live, bounded and ....

Huynh, D.T.: Commutative Grammars: The Complexity of Uniform Word Problems. Information and Control 57 (1983), 21--39.

....result has been proved for many other net classes, see again [5] for a survey) In the second part of the paper we apply the results of the first part to two different problems in the areas of formal languages and process algebras. The first problem concerns commutative grammars. Huynh proved in [13] the NPcompleteness of the uniform word problem for commutative context free grammars. The proof is rather involved (8 journal pages) It is easy to see that this problem coincides with the reachability problem for communication free nets. Therefore, our results lead immediately to a new and ....

....A Gamma w iff w is a reachable marking of the Petri net translation of G c . So the uniform word problem for ccf grammars can be reduced in linear time to the reachability problem for communication free Petri nets, and vice versa. Therefore, we have a new proof for the following result of [13]: Theorem 4.1. The uniform word problem for commutative context free grammars is NPcomplete. The connection between commutative context free grammars and Petri nets was pointed out in [13] but not used. The proof of membership in NP of [13] takes 8 journal pages, and Javier Esparza Petri ....

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Huynh, D.T.: "Commutative Grammars: The Complexity of Uniform Word Problems", Information and Control 57, 1983, 21--39.

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Huynh, D.T.: "Commutative Grammars: The Complexity of Uniform Word Problems", Information and Control 57, 1983, 21--39.

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D.T. Huynh. Commutative grammars: The complexity of uniform word problems. Information and Control, 57(1):21--39, 1983.

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D.T. Huynh. Commutative grammars: The complexity of uniform word problems. Information and Control, 57:21--39, 1983.

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D.T. Huynh. Commutative grammars: The complexity of uniform word problems. Information and Control, 57:21--39, 1983.

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D.T. Huynh. Commutative grammars: The complexity of uniform word problems. Information and Control, 57:21--39, 1983.

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