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Complexity of unification in free groups and free semi-groups

A. Koscielski, L. Pacholski
Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science  
The exponent of periodicity is an important factor in estimates of complexity of word-unification algorithms.  ...  Moreover we give some evidence that, contrary to the common belief, the algorithm deciding satisfiability of equations in free groups, given by Makanin in not primitive recursive.  ...  in free groups.  ... 
doi:10.1109/fscs.1990.89605 dblp:conf/focs/KoscielskiP90 fatcat:jncrappatvbtphyzraqdma4r24

The Complexity of Equivariant Unification [chapter]

James Cheney
2004 Lecture Notes in Computer Science  
In this paper, we study the complexity of the decision problem for equivariant unification and matching. We show that these problems are NPcomplete in general.  ...  However, when one of the terms is essentially firstorder, equivariant and nominal unification coincide.  ...  programming, and term rewriting in nominal logic.  ... 
doi:10.1007/978-3-540-27836-8_30 fatcat:tgklvhk5ane45cdq7dqwxrjuvi

Adding homomorphisms to commutative/monoidal theories or how algebra can help in equational unification [chapter]

Franz Baader, Werner Nutt
1991 Lecture Notes in Computer Science  
The class encompasses important examples like the theories of abelian monoids , idempotent abelian monoids , and abelian groups .  ...  The two results illustrate how using algebraic machinery can lead to general results and elegant proofs in unification theory.  ...  The theory AMH is AM(h*) where h* stands for the free monoid in one generator, and AMIn is AM(Z2) where Z2 stands for the cyclic group of order 2, i.e., Z2 consists of two elements e and h, and the multiplication  ... 
doi:10.1007/3-540-53904-2_91 fatcat:6jzlkhtkxnccfmbmwzr3xccnra

Page 7646 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
Lett. 52 (1994), no.2, 61-68. 95m:68020b 68N15 Rittri, Mikael (S-CHAL-C; Goteborg) Corrigendum: “Semi-unification of two terms in abelian groups”. Inform. Process. Lett. 53 (1995), no.4, 235.  ...  of two terms in abelian groups.  ... 

Page 947 of Mathematical Reviews Vol. , Issue 82c [page]

1982 Mathematical Reviews  
Here we discuss the degrees of the halting, word and confluence problems for modular machines both for their own sake and in the hope that the results may be useful in group theory.  ...  Square-free and cube-free colorings of the ordinals. Pacific J. Math. 89 (1980), no. 1, 137-141.  ... 

Hints in Unification [chapter]

Andrea Asperti, Wilmer Ricciotti, Claudio Sacerdoti Coen, Enrico Tassi
2009 Lecture Notes in Computer Science  
We claim that all these mechanisms are particular instances of a simpler and more general technique, just consisting in providing suitable hints to the unification procedure underlying type inference.  ...  This allows a simple, modular and not intrusive implementation of all the above mentioned techniques, opening at the same time innovative and unexpected perspectives on its possible applications.  ...  ≡ o and ? f i ? ≡ o are extremely complex.  ... 
doi:10.1007/978-3-642-03359-9_8 fatcat:ibgqhnwhvfff5jradae242oyuu

Page 7066 of Mathematical Reviews Vol. , Issue 92m [page]

1992 Mathematical Reviews  
{For the entire collection see MR 92h:68008.} 92m:68043 68Q25 20F10 68Q20 Koscielski, Antoni (PL-WROC-C); Pacholski, Leszek (PL-PAW) Complexity of unification in free groups and free semi-groups. 31st  ...  Summary: “The exponent of periodicity is an important factor in estimates of complexity of word-unification algorithms.  ... 

A Brief Review of Three-Family Grand Unification in String Theory [article]

Zurab Kakushadze
1998 arXiv   pre-print
We briefly review the status of three-family grand unified string models.  ...  The situation is similar for embedding unification within a semi-simple 10 gauge group G ⊃ SU (3) c ⊗ SU (2) w ⊗ U (1) Y (e.g., SU (5) ⊗ U (1)).  ...  group G, and the gauge coupling of G meets with α G as shown in Fig.1b  ... 
arXiv:hep-th/9807240v1 fatcat:l3vom4cs7bc3zdzczudvxwlie4

Unification without Unification [article]

Neal Weiner
2001 arXiv   pre-print
In this "collapsed GUT" mechanism, unification of coupling constants in the low energy theory is expected, but proton decay and the doublet/triplet splitting problem are entirely absent.  ...  This is often taken to imply that the standard model gauge group is embedded into some larger simple group in which quarks and leptons are placed in the same multiplet.  ...  Kaplan and Yasunori Nomura for useful discussions, and to Ann Nelson for reviewing the manuscript and useful discussions.  ... 
arXiv:hep-ph/0106097v3 fatcat:tmw75qkdpvd7hhqh7md4lfzltm

Source-Tracking Unification [chapter]

Venkatesh Choppella, Christopher T. Haynes
2003 Lecture Notes in Computer Science  
Such a framework is useful for diagnosing unification-based systems, including debugging of type errors in programs and the generation of success and failure proofs in logic programming.  ...  The semantics of deductions are paths over a unification graph whose labels form the suffix language of a semi-Dyck set.  ...  Acknowledgment Critical feedback from the anonymous referees also helped considerably in improving the paper.  ... 
doi:10.1007/978-3-540-45085-6_39 fatcat:56ievgbgqnfcxhbo5hx56bd66m

Source-tracking unification

Venkatesh Choppella, Christopher T. Haynes
2005 Information and Computation  
Such a framework is useful for diagnosing unification-based systems, including debugging of type errors in programs and the generation of success and failure proofs in logic programming.  ...  The semantics of deductions are paths over a unification graph whose labels form the suffix language of a semi-Dyck set.  ...  Acknowledgment Critical feedback from the anonymous referees also helped considerably in improving the paper.  ... 
doi:10.1016/j.ic.2004.10.013 fatcat:sg4x4pzierg3tgrqefcq5bchce

The second string (phenomenology) revolution

Luis E Ibáñez
2000 Classical and quantum gravity  
In addition, semi-realistic three generation models have recently been constructed starting with Type IIB compact orientifolds.  ...  I briefly discuss some of these developements which represent a revolution in our understanding of string phenomenology.  ...  Uranga and G. Violero for an enjoyable collaboration.  ... 
doi:10.1088/0264-9381/17/5/321 fatcat:2sytb5xl2nfc3mm6qfxr6j5ucm

Three-family grand unification in string theory

Zurab Kakushadze
1998 Nuclear Physics B - Proceedings Supplements  
We briefly discuss the status of three-family grand unified string models.  ...  The situation is similar for embedding unification within a semi-simple [6] gauge group G ⊃ SU (3) c ⊗SU (2) w ⊗U (1) Y (e.g., SU (5) ⊗ U (1)).  ...  The state of affairs is quite different if one tries to embed grand unification within a simple gauge group G ⊃ SU (3) c ⊗ SU (2) w ⊗ U (1) Y .  ... 
doi:10.1016/s0920-5632(97)00655-5 fatcat:3ojzobnxtzbtdfrtxjkytf2dxu

Theories of Homomorphic Encryption, Unification, and the Finite Variant Property

Fan Yang, Santiago Escobar, Catherine Meadows, José Meseguer, Paliath Narendran
2014 Proceedings of the 16th International Symposium on Principles and Practice of Declarative Programming - PPDP '14  
This new verification procedure also allows us to construct a rough metric of the complexity of a theory with respect to variant unification, or variant complexity.  ...  In this paper we address this problem by studying various approximations of homomorphic encryption over an Abelian group.  ...  Theory of Homomorphic Encryption over a Free Operator Theory of Homomorphic Encryption over a Pre-Group In this section, we extend TH & to be an homomorphic encryption over a pre-group.  ... 
doi:10.1145/2643135.2643154 dblp:conf/ppdp/YangEMMN14 fatcat:ss5awwz6wffnnlp6i67rg5svcu

Some Remarks On Superstring Phenomenology [article]

Zurab Kakushadze, S.-H. Henry Tye
1995 arXiv   pre-print
The present status of superstring phenomenology is briefly discussed.  ...  This is probably because both the NAHE set and a higher-level gauge group need lots of space, which is not available within the free fermionic construction.  ...  Since the rank of the gauge group of the hidden (plus semi-hidden) sector of such string models can be as large as 17, the choices is numerous.  ... 
arXiv:hep-th/9512155v1 fatcat:vepfg4uotjeftkss2get7w5dlm
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