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Page 467 of Mathematical Reviews Vol. , Issue 89A [page]

1989 Mathematical Reviews  
Summary: “We prove that the parsing problem for bracket context- free languages can be solved in logn time using n/logn processors on a parallel random access machine without write conflicts (P- RAM).  ...  Then the complexity of some problems involving the one-sided distributivity axiom D,, the two-sided distributivity axiom D, and the axiom U (x +1 =1+*x = x) is investigated.  ... 

A linear algorithm for MLL proof net correctness and sequentialization

Stefano Guerrini
2011 Theoretical Computer Science  
As for term unification, a direct implementation of the unification criterion leads to a quasi-linear algorithm.  ...  The algorithm is essentially a reformulation of the Danos contractibility criterion in terms of a sort of unification.  ...  Every sequential unification reduction corresponds to a (parallel) unification reduction.  ... 
doi:10.1016/j.tcs.2010.12.021 fatcat:g7rx3q62wfcxzo5eaq2wkt7ul4

On the relationship of congruence closureand unification

Paris C. Kanellakis, Peter Z. Revesz
1989 Journal of symbolic computation  
Using parallel complexity we also clarify the relationship of unification closure and the testing of deterministic finite automata for equivalence. 0747-7 ] 71/89/030427 + 18 $0320/0 9  ...  of term unification.  ...  The problem with this algorithm as a general parallel algorithm is that Steps 2 and 3 migh~ have to alternate O(N) times (Dwork et al. 1984 For the k > 0 case all we have to note is that, !  ... 
doi:10.1016/s0747-7171(89)80018-5 fatcat:mrzlcieccvf2xizftityf5baqq

Describing Lambda Terms in Context Unification [chapter]

Joachim Niehren, Mateu Villaret
2005 Lecture Notes in Computer Science  
We show that lambda binding plus parallelism constraints can be expressed in context unification with tree regular constraints.  ...  Parallelism constraints alone are known to have the same expressive power as the language of context unification. Lambda binding constraints however were never investigated in that framework.  ...  This axiom coincides for c and c −1 .  ... 
doi:10.1007/11422532_15 fatcat:dd5pbitrc5bobj45itzobdw63y

Page 3151 of Mathematical Reviews Vol. , Issue 90F [page]

1990 Mathematical Reviews  
Let T be any set of axioms be- tween D, and H10, where H10 is the set of axioms for number theory.  ...  Resolution- based systems for the multimodal (epistemic logic) system S$4(n) and for two other (extended) epistemic logics are discussed, the proofs of their properties being outlined.  ... 

Parallelism Constraints [chapter]

Katrin Erk, Joachim Niehren
2000 Lecture Notes in Computer Science  
Parallelism constraints are logical desciptions of trees. They are as expressive as context unification, i.e. second-order linear unification.  ...  We present a semi-decision procedure enumerating all "most general unifiers" of a parallelism constraint and prove it sound and complete.  ...  Parallelism constraints differ from context unification in their perspective on trees.  ... 
doi:10.1007/10721975_8 fatcat:dyqef76aovcufj7ldv7nizftfi

Unification nets: canonical proof net quantifiers [article]

Dominic J. D. Hughes
2018 arXiv   pre-print
These results extend beyond MLL1 via a broader methodological insight: for canonical quantifiers, the standard parallel/sequential dichotomy of proof nets fails; an implicit/explicit witness dichotomy  ...  Unification nets solve both problems: (1) cut elimination is local and linear-time, and (2) cut-free unification nets grow linearly with the size of the sequent.  ...  The formal unification problem is as follows. An axiom link between P(s 1 , . . . , s n ) and P(t 1 , . . . , t n ) determines n equations s i = t i .  ... 
arXiv:1802.03224v1 fatcat:3mz5xcqzuvbzljrllx5lzajgwq

Comparing Approaches To Resolution Based Higher-Order Theorem Proving

Christoph Benzmüller
2002 Synthese  
can completely avoid additional extensionality axioms.  ...  With the help of examples we illustrate the parallels and differences of the extensionality treatment of these approaches and demonstrate that extensional higher-order resolution is the sole approach that  ...  B 3 ] ∨ . . . ∨ [B n−1 = ? B n ]. Unification and Splitting.  ... 
doi:10.1023/a:1020840027781 fatcat:sghuiqlg6vd3dhgr2f6clo4ssq

An algorithm for distributive unification [chapter]

Manfred Schmidt-Schauß
1996 Lecture Notes in Computer Science  
We consider unification of terms under the equational theory of two-sided distributivity D with the axioms x*(y+z) = x*y + x*z and (x+y)*z = x*z + y*z.  ...  An element in I D1 has a u n i q u e factorization, if there is only one representation as a product of prime elements, up to commutativity.  ...  Furthermore it provides a theory generated by a subset of the Peanoaxioms, which has a decidable unification problem.  ... 
doi:10.1007/3-540-61464-8_60 fatcat:webxvrl4nzb6xfpnnsflrbakea

The undecidability of k-provability

Samuel R. Buss
1991 Annals of Pure and Applied Logic  
Indeed, for every r.e. set X there is a formula @(I) and an integer k such that for all n, $(SnO) has a proof of Sk sequents if and only if n E X.  ...  So we let N be k + 29m -2; we need to show that if the unification problem has no solution then any proof of @ requires at least N + 1 lines.  ...  Because ni and n,, parallel each other for as long as possible (by condition (Rl)), they will diverge at an v:left inference while travelling upwards.  ... 
doi:10.1016/0168-0072(91)90059-u fatcat:gjdkgthtynfzzeml2u7k2fkfkm

Page 7289 of Mathematical Reviews Vol. , Issue 2004i [page]

2004 Mathematical Reviews  
Eugenia (I-GENO-IF; Genoa) N -axioms parallel unification. (English summary) Special issue on concurrency specification and programming, Part 2 (Berlin, 2002). Fund.  ...  N-axioms unification extends the structure of uni- fication inputs and brings out the notion of interleaving variable as a special repeated variable which serializes independent com- putations.  ... 

Unification: a multidisciplinary survey

Kevin Knight
1989 ACM Computing Surveys  
applications of unification.  ...  Other topics covered are resolution, higher order logic, the occur check, infinite terms, feature structures, equational theories, inheritance, parallel algorithms, generalization, lattices, and other  ...  By way of the parallel computation thesis [Goldschlager 19781 , which relates sequential space to parallel time, this result could have led to a log2 n parallel time algorithm for unification.  ... 
doi:10.1145/62029.62030 fatcat:u4ieq3eekzg25fgpxsaebyktkm

Rational Unification in 28 Characters

Pietro Cenciarelli, Alessandro Tiberi
2005 Electronical Notes in Theoretical Computer Science  
We present a case study where Synchronising Graphs, a system of parallel graph transformation, are used to solve the syntactic unification problem for first order rational terms (with possibly infinite  ...  The behaviour of parallel, possibly distributed systems is specified in SG by a set of axioms.  ...  In Section 4 we write a program (two axioms) of 28 characters in SG to solve the problem of syntactic unification, and show it at work with an example.  ... 
doi:10.1016/j.entcs.2005.02.013 fatcat:zfucl7kx4fgvjlckktiqc7ovk4

Unification theory [chapter]

Franz Baader
1992 Lecture Notes in Computer Science  
In particular, this implies that it is very unlikely that an efficient parallel unification algorithm exists. In this section we review the major approaches to syntactic unification.  ...  This is achieved by replacing the use of syntactic unification in the resolution step by equational unification, i.e., unification modulo the equational theory induced by the axioms to be built in.  ... 
doi:10.1007/3-540-55124-7_5 fatcat:yneggkjxfreqbheexpvvm5flla

Automation of Higher-Order Logic [chapter]

Christoph Benzmüller, Dale Miller
2014 Handbook of the History of Logic  
∃M ∃N.λxλy.f (M xy) = λxλy.N y ∃M ∀x∀y.f (M xy) = f y ∃M ∀x.λy.M xy = λy.M yx ∃M ∃N.∀x∀y.M xy = N y are all pattern unification problems.  ...  Unification of simply typed λ-terms Traditionally, the unification of simply typed λ-terms can be described as proving the formula ∃x 1 τ1 . . . ∃x n τn . t 1 = s 1 ∧ · · · ∧ t m = s m (n, m ≥ 0).  ... 
doi:10.1016/b978-0-444-51624-4.50005-8 fatcat:jfcztdvymjfujg3bzb2rq2qyzy
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