A Polynomial Time Extension of Parallel Multiple Context-Free Grammar

Abstract. It is already known that parallel multiple context-free grammar (PMCFG) [1] is an instance of the equivalent formalisms simple literal movement grammar (sLMG) [2,3] and range concatenation grammar (RCG) [4,5]. In this paper we show that by adding the single operation of intersection, borrowed from conjunctive grammar [6], PMCFG becomes equivalent to sLMG and RCG. As a corollary we get that PMCFG with intersection describe exactly the class of languages recognizable in polynomial time. The layout of this paper is as follows. The first section contains definitions of the basic grammar formalisms we are interested in. The second section introduces the intersection operation for PMCFG. The third section contains the main result of the paper – that PMCFG extended with the intersection operation is equivalent to simple LMG and RCG. The fourth and last section is a small discussion of the results. 1 GCFG, PMCFG, sLMG and RCG

• Type: Conference
• Year: 2005
• Where: LACL
• Authors: Peter Ljunglöf
• Keywords: Grammar, Intersection Operation, LACL 2005, Multiple Context-free Grammar, Natural Language Processing