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Bounded Second-Order Unification Is NP-Complete
[chapter]

2006
*
Lecture Notes in Computer Science
*

It

doi:10.1007/11805618_30
fatcat:3vv2y2svezgjdaddzknhvqjr34
*is*already known that*Bounded**Second*-*Order**Unification**is*decidable and*NP*-hard, whereas general*Second*-*Order**Unification**is*undecidable. ... We prove that*Bounded**Second*-*Order**Unification**is**NP*-*complete*, provided that m*is*given in unary encoding, by proving that a size-minimal solution can be represented in polynomial space, and then applying ...*Bounded**Second*-*Order**Unification**is**NP*-*complete*. Proof: For any equation E, and any size-minimal solution σ, there exists a STG of polynomial size in |E| that generates σ(X), for every X ∈ V ar(E). ...##
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Stratified Context Unification Is NP-Complete
[chapter]

2006
*
Lecture Notes in Computer Science
*

A corollary of our result

doi:10.1007/11814771_8
fatcat:zbhcjiuxjrewxajajwmjsmygki
*is*that solvability of rewrite constraints*is**NP*-*complete*. ... Context*Unification**is*the problem to decide for a given set of*second*-*order*equations E where all*second*-*order*variables are unary, whether there exists a unifier, such that for every*second*-*order*variable ... Conclusion and Further Research We have shown that stratified context*unification**is**NP*-*complete*by exploiting compaction of terms and polynomial comparison of the compactions using singleton tree grammars ...##
###
Simplifying the signature in second-order unification

2009
*
Applicable Algebra in Engineering, Communication and Computing
*

Our work simplifies the study of

doi:10.1007/s00200-009-0106-4
fatcat:ltrscory3nb7bdrfjy5jjoof2q
*Second*-*Order**Unification*and some of its variants, like Context*Unification*and*Bounded**Second*-*Order**Unification*. ... If all symbols are monadic, then the problem*is**NP*-*complete*, whereas it*is*enough to have just one binary constant to lose decidability. ... Theorem 3 Decidability of*Bounded**Second*-*Order**Unification*can be*NP*-reduced to decidability of*Bounded**Second*-*Order**Unification*with just one binary function symbol, and constants. ...##
###
Page 60 of Journal of Research and Practice in Information Technology Vol. 15, Issue 2
[page]

1983
*
Journal of Research and Practice in Information Technology
*

Therefore, the

*complete*value of N1*is*described by a pair consisting of a pointer to the term*np*(N) and another poin- ter to the frame in which N*is**bound*. ... Similarly, when the two terms corresponding to the*second*arguments of terms (1) and (2) are matched, V will become*bound*to ‘vp(v(likes),*np*(mary))’. ...##
###
Complexity of the Higher Order Matching
[chapter]

1999
*
Lecture Notes in Computer Science
*

We obtain this way already known

doi:10.1007/3-540-48660-7_6
fatcat:w4ykjjdclbak5c72c5toaz46ci
*NP*-hardness*bounds*for the*order*two and three and a new result that the fourth*order*matching*is*NEXPTIME-hard. , 82-96. † Supported by KBN grant 8 T 11C 029 13. 1 Since ... the term "pattern" has multiple meanings in the theory of higher*order**unification*, e.g., the one introduced by Dale Miller [15] , we would rather avoid it when speaking about*unification*of an arbitrary ... Thus: Corollary 1*Second**order*pure*unification*(in particular matching)*is*in*NP*.*Second**order*pure*unification*(in particular matching) with*bounded*number of variables*is*in PTIME. ...##
###
Restricted Unification in the DL EL

2021
*
International Workshop on Description Logics
*

The complexity of deciding unifiability

dblp:conf/dlog/BaaderR21
fatcat:rwzldipnive5bpahbu4d3x3g5m
*is*ExpTime-*complete*for FL0 and*NP*-*complete*for EL. ... the decision problem stays*NP*-*complete*. ...*Unification*in EL*is**NP*-*complete*. ...##
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Tractable and Intractable Second-Order Matching Problems
[chapter]

1999
*
Lecture Notes in Computer Science
*

It

doi:10.1007/3-540-48686-0_43
fatcat:kif2eqafhvcnvnbrfqbawgsgmm
*is*well-known that the*second*-*order*matching problem*is**NP*-*complete*. ... Then, we show that the*second*-*order*matching problem*is**NP*-*complete*for a unary predicate, a unary ground, a ternary function-free predicate, a binary function-free ground, and an 1-fv predicate matching ... It*is*also well-known that the*second*-*order*matching problem*is**NP*-*complete*[2] . Huet and Lang [14] have designed a*complete*and nonredundant*second*-*order*matching algorithm. ...##
###
Tractable and intractable second-order matching problems

2004
*
Journal of symbolic computation
*

It

doi:10.1016/j.jsc.2003.09.002
fatcat:c3mvlslzrzdbrexciaqbxd6uau
*is*well-known that the*second*-*order*matching problem*is**NP*-*complete*. ... Then, we show that the*second*-*order*matching problem*is**NP*-*complete*for a unary predicate, a unary ground, a ternary function-free predicate, a binary function-free ground, and an 1-fv predicate matching ... It*is*also well-known that the*second*-*order*matching problem*is**NP*-*complete*[2] . Huet and Lang [14] have designed a*complete*and nonredundant*second*-*order*matching algorithm. ...##
###
Page 2056 of Mathematical Reviews Vol. , Issue 2003C
[page]

2003
*
Mathematical Reviews
*

2003c:68091
error probabilistic

*ordered*branching programs*is**NP*-*complete*. ... Summary: “Context*unification**is*a variant of*second**order*uni- fication and also a generalization of string*unification*. Currently it*is*not known whether context*unification**is*decidable. ...##
###
Linear Higher-Order Matching Is NP-Complete
[chapter]

2000
*
Lecture Notes in Computer Science
*

We prove that this problem

doi:10.1007/10721975_9
fatcat:a6y3c5ebj5exjapfphk4wuhxci
*is*decidable by showing that it belongs to*NP*. Then we prove that this problem*is*in fact*NP*-*complete*. Finally, we discuss some heuristics for a practical algorithm. ... We consider the problem of higher-*order*matching restricted to the set of linear λ-terms (i.e., λ-terms where each abstraction λx. M*is*such that there*is*exactly one free occurrence of x in M ). ... Whether linear higher-*order**unification**is*decidable*is*an open problem related, in the*second*-*order*case, to context*unification*[11] . ...##
###
Matching in the Description Logic FL0 with respect to General TBoxes (Extended abstract)

2019
*
International Workshop on Description Logics
*

Whereas in EL both matching [6] and

dblp:conf/dlog/BaaderGM19
fatcat:lk6q57liybemncvd2ydpwo4xry
*unification*[7] are*NP*-*complete*problems, the complexity of these problems differs significantly for FL 0 : matching*is*polynomial, but*unification**is*ExpTime-*complete*... TBoxes*is*Exp-Time-*complete*[3] , ExpTime-hardness of this problem*is*clear. The first main contribution of this paper*is*thus to show the ExpTime upper*bound*. ...##
###
Assessing Complexity Results in Feature Theories
[article]

1995
*
arXiv
*
pre-print

On the one hand, the complexity of feature theories does not provide an upper

arXiv:cmp-lg/9503022v1
fatcat:5xx6mc6jx5hfdh7ok2cqfqijjm
*bound*for the complexity of such*unification*grammars. ... On the other hand, the complexity of feature theories need not provide a lower*bound*. Therefore, we argue for formalisms that describe actual*unification*grammars instead of feature theories. ... An additional*NP*upper*bound**is*proven for an arbitrary string and grammar, which results in an*NP*-*complete*recognition problem. ...##
###
Monadic Second-Order Unification Is NP-Complete
[chapter]

2004
*
Lecture Notes in Computer Science
*

It

doi:10.1007/978-3-540-25979-4_4
fatcat:cygu7illbvap7kxyhgkn6rtvbe
*is*already known that*Bounded**Second*-*Order**Unification**is*decidable and*NP*-hard, whereas general*Second*-*Order**Unification**is*undecidable. ... We prove that*Bounded**Second*-*Order**Unification**is**NP*-*complete*, provided that m*is*given in unary encoding, by proving that a size-minimal solution can be represented in polynomial space, and then applying ...*Bounded**Second*-*Order**Unification**is**NP*-*complete*. Proof: For any equation E, and any size-minimal solution σ, there exists a STG of polynomial size in |E| that generates σ(X), for every X ∈ V ar(E). ...##
###
Scope and Situation Binding in LTAG Using Semantic Unification

2008
*
Research on Language and Computation
*

Then, within this framework, an analysis of scope

doi:10.1007/s11168-008-9046-6
fatcat:ok7gp4jounbchfmukd7dk4qhj4
*is*proposed that accounts for the different scopal properties of quantifiers, adverbs, raising verbs and attitude verbs. ... In general, the complexity of disambiguating expressions with scope constraints of the form x ≤ y*is**NP*-*complete*. ... Furthermore, the*second*situation within sometimes must be locally*bound*by the ∀s-quantification of think, yielding ∃s [s s]; if it could be distantly*bound*and represented as ∃s [s s 0 ], the sentence ...##
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Page 7594 of Mathematical Reviews Vol. , Issue 2004j
[page]

2004
*
Mathematical Reviews
*

best known lower

*bound*complexity*is*known to be*NP*-hard. ... The context*unification*problem (CUP) can be seen as a variant of*second*-*order**unification*or as a generalization of the string*unification*problem. ...
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