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ProductFree Lambek Calculus Is NPComplete
 In Logical Foundations of Computer Science. Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
, 2009
"... In this paper we prove that the derivability problems for productfree Lambek calculus and productfree Lambek calculus allowing empty premises are NPcomplete. Also we introduce a new derivability characterization for these calculi. ..."
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Cited by 4 (0 self)
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In this paper we prove that the derivability problems for productfree Lambek calculus and productfree Lambek calculus allowing empty premises are NPcomplete. Also we introduce a new derivability characterization for these calculi.
Term Graphs and the NPcompleteness of the ProductFree Lambek Calculus
"... Abstract. We provide a graphical representation of proofs in the productfree Lambek calculus, called term graphs, that is related to several other proof net presentations. The advantage of term graphs is that they are very simple compared to the others. We use this advantage to provide an NPcomple ..."
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Abstract. We provide a graphical representation of proofs in the productfree Lambek calculus, called term graphs, that is related to several other proof net presentations. The advantage of term graphs is that they are very simple compared to the others. We use this advantage to provide an NPcompleteness
Efficient Parsing with the ProductFree Lambek Calculus
"... This paper provides a parsing algorithm for the Lambek calculus which is polynomial time for a more general fragment of the Lambek calculus than any previously known algorithm. The algorithm runs in worstcase time O(n5) when restricted to a certain fragment of the Lambek calculus which is motivated ..."
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Cited by 1 (1 self)
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This paper provides a parsing algorithm for the Lambek calculus which is polynomial time for a more general fragment of the Lambek calculus than any previously known algorithm. The algorithm runs in worstcase time O(n5) when restricted to a certain fragment of the Lambek calculus which
Lambek calculus is npcomplete
 Theoretical Computer Science
, 2003
"... We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L ∗ the derivability problem is NPcomplete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NPcomplete. ..."
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Cited by 34 (0 self)
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We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L ∗ the derivability problem is NPcomplete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NPcomplete.
Productfree Lambek calculus and contextfree grammars
 The Journal of Symbolic Logic
, 1997
"... In this paper we prove the Chomsky Conjecture (all languages recognized by the Lambek calculus are contextfree) for both the full Lambek calculus and its productfree fragment. For the latter case we present a construction of contextfree grammars involving only productfree types. ..."
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Cited by 24 (0 self)
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In this paper we prove the Chomsky Conjecture (all languages recognized by the Lambek calculus are contextfree) for both the full Lambek calculus and its productfree fragment. For the latter case we present a construction of contextfree grammars involving only productfree types.
Parsing for Semidirectional Lambek Grammar is NPComplete
, 1996
"... We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call semidirectional. In semidirectional Lambek calculus SDL there is an additional non directional abstraction rule allowing the formula abstracted over to appear anywhere in the premise ..."
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Cited by 1 (0 self)
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sequent's lefthand side, thus permitting nonperipheral extraction. SDL grammars are able to generate each contextfree language and more than that. We show that the parsing prob lem for semidirectional Lambek Grammar is NPcomplete by a reduction of the 3Partition problem.
Computational LambdaCalculus and Monads
, 1988
"... The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise the ..."
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Cited by 505 (7 self)
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The calculus is considered an useful mathematical tool in the study of programming languages, since programs can be identified with terms. However, if one goes further and uses fijconversion to prove equivalence of programs, then a gross simplification 1 is introduced, that may jeopardise
Lambek Calculus with Nonlogical Axioms
 Language and Grammar, Studies in Mathematical Linguistics and Natural Language
, 2002
"... We study Nonassociative Lambek Calculus and Associative Lambek Calculus enriched with nitely many nonlogical axioms. We prove that the nonassociative systems are decidable in polynomial time and generate contextfree languages. In [1] it has been shown that nite axiomatic extensions of Associa ..."
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Cited by 14 (10 self)
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We study Nonassociative Lambek Calculus and Associative Lambek Calculus enriched with nitely many nonlogical axioms. We prove that the nonassociative systems are decidable in polynomial time and generate contextfree languages. In [1] it has been shown that nite axiomatic extensions
Symbolic Model Checking for Realtime Systems
 INFORMATION AND COMPUTATION
, 1992
"... We describe finitestate programs over realnumbered time in a guardedcommand language with realvalued clocks or, equivalently, as finite automata with realvalued clocks. Model checking answers the question which states of a realtime program satisfy a branchingtime specification (given in an ..."
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Cited by 574 (50 self)
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in an extension of CTL with clock variables). We develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates, without constructing the state space. For this purpose, we introduce a calculus on computation trees over realnumbered time. Unfortunately
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