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Application of automated deduction to the search for single axioms for exponent groups [chapter]

William McCune, Larry Wos
Logic Programming and Automated Reasoning  
The results include single axioms, some with the identity and _"_ others without, for groups of exponents 3, 4, 5, and 7, and a general form for single axioms for groups of odd exponent.  ...  The results were obtained by using the programs in three separate ways: as a symbol,ic calculator, to search for proofs, and to search for counterexamples.  ...  deduction, and automated reasoning on less-focused search.  ... 
doi:10.1007/bfb0013055 dblp:conf/lpar/McCuneW92 fatcat:t33nsxvxzfee5pnuq5pvrxzrme

SINGLE AXIOMS: WITH AND WITHOUT COMPUTERS

WILLIAM MCCUNE
2000 Computer Mathematics  
A shortest single axiom for Boolean groups was already known. 8 In 1992, the Wos and I presented a schema for short axioms for groups of odd exponent. 16 For exponent 3 groups, the schema produces  ...  However, straightforward application of the method usually yields single axioms of enormous length.  ... 
doi:10.1142/9789812791962_0013 fatcat:6iambqypgra5do3kwmfctilawa

The Legacy of a Great Researcher [chapter]

Larry Wos
2013 Lecture Notes in Computer Science  
This article presents examples of the monumental contributions of Bill McCune to mathematics, logic, computer science, and especially automated reasoning.  ...  The examples are presented in the form of short stories and recollections of the author during his long association with Bill.  ...  Government retains for itself, and others acting on its behalf, a paid-up, nonexclusive, irrevocable worldwide license in said article to reproduce, prepare derivative works, distribute copies to the public  ... 
doi:10.1007/978-3-642-36675-8_1 fatcat:6nhkdcslprhkbl6ciehihqorwq

The shortest single axioms for groups of exponent 4

K. Kunen
1995 Computers and Mathematics with Applications  
We study equations of the form (c~ = x), which are single axioms for groups of exponent 4, where a is a term in product only.  ...  We also present an improvement on Neumann's scheme for single axioms for varieties of groups.  ...  Actually, he found a general scheme for single axioms for any variety of groups, but the single axioms for exponent n groups produced as instances of this scheme are quite large, and it is natural to ask  ... 
doi:10.1016/0898-1221(94)00212-4 fatcat:jzv3guc24zf55ebmeu6nkgwio4

Single identities for ternary Boolean algebras

R. Padmanabhan, W. McCune
1995 Computers and Mathematics with Applications  
The first single axiom was found algebraically by a previous technique of Padmanabhan and Quackenbush; then simpler single axioms were found by using the automated reasoning program OTTER. ieywords--Automated  ...  We present the first known single axioms for ternary Boolean algebra.  ...  SEARCHING FOR A SIMPLER SINGLE AXIOM FOR TBAS OTTER  ... 
doi:10.1016/0898-1221(94)00213-5 fatcat:h7ot6sxacfau5pzlv3lp3muf3e

Page 1630 of Mathematical Reviews Vol. , Issue 94c [page]

1994 Mathematical Reviews  
for single axioms for exponent groups (131-136); Hai Ping Ko and Mark E.  ...  Fermiiller, Resolution for many-valued logics (107- 118); Peter Baumgartner, An ordered theory resolution calculus (119-130); William McCune and Larry Wos, Application of au- tomated deduction to the search  ... 

Automated Deduction: Looking Ahead

Donald W. Loveland
1999 The AI Magazine  
In this article, the body of a report on automated deduction is presented that notes some significant achievements and takes a studied look at the future of the field. Articles  ...  ; Kamal Abdali, program director, Numeric, Symbolic, and Geometric Besides the contributions of the participants during the workshop itself, there were many added contributions of time and effort to  ...  Acknowledgments The workshop on which this article and the underlying report are based was attended by 23 U.S. researchers, listed here; Wolfgang Bibel from the Technische Hochschule Darmstadt, Germany  ... 
doi:10.1609/aimag.v20i1.1442 dblp:journals/aim/Loveland99 fatcat:quvjcbyot5fzfga27lzwp6pqwa

The Flowering of Automated Reasoning [chapter]

Larry Wos
2005 Lecture Notes in Computer Science  
This article celebrates with obvious joy the role automated reasoning now plays for mathematics and logic.  ...  The contributions to mathematics and logic made with an automated reasoning assistant are many, diverse, often signi cant, and of the type Hilbert would indeed have found most pleasurable.  ...  The theorem (actually too strong a classi cation) asks for a proof of commutativity for groups of exponent 2 (those in which the square of x is the identity e).  ... 
doi:10.1007/978-3-540-32254-2_13 fatcat:p5hhow7whnevtfjmw4imhoakm4

The Mechanization of Mathematics [chapter]

Michael J. Beeson
2004 Alan Turing: Life and Legacy of a Great Thinker  
Turing showed that a complete reduction of mathematics to computation is not possible, but nevertheless the art and science of automated deduction has made progress.  ...  The mechanization of mathematics refers to the use of computers to find, or to help find, mathematical proofs.  ...  I am grateful to the following people, who read drafts and suggested changes: Nadia Ghamrawi, Marvin Jay Greenberg, Mike Pallesen, and Larry Wos.  ... 
doi:10.1007/978-3-662-05642-4_5 fatcat:uwbuvf4bebf7dlvo55l75hd2km

Mechanization of Mathematics

W. G. BICKLEY
1950 Nature  
Turing showed that a complete reduction of mathematics to computation is not possible, but nevertheless the art and science of automated deduction has made progress.  ...  The mechanization of mathematics refers to the use of computers to find, or to help find, mathematical proofs.  ...  I am grateful to the following people, who read drafts and suggested changes: Nadia Ghamrawi, Marvin Jay Greenberg, Mike Pallesen, and Larry Wos.  ... 
doi:10.1038/1661087a0 fatcat:67maf3rrvjg73mivang5isihza

Automated Verification of Group Key Agreement Protocols

Benedikt Schmidt, Ralf Sasse, Cas Cremers, David Basin
2014 2014 IEEE Symposium on Security and Privacy  
We automatically verify a set of protocols, including the STR, group Joux, and GDH protocols, thereby demonstrating the effectiveness of our approach. STR Group Joux Joux  ...  Our support for AC-operators enables protocol specifications to use multisets, natural numbers, and finite maps.  ...  Nodes 4-8 are instances of message deduction rules and denote that the adversary receives a pair of a group element and an exponent, raises the first component to the power of the second component, and  ... 
doi:10.1109/sp.2014.19 dblp:conf/sp/SchmidtSCB14 fatcat:t5c3nd2mifcirbrd3rnmhqt32a

Maximal Models and Refutation Completeness: Semidecision Procedures in Automatic Theorem Proving [chapter]

L. T. Wos, G. A. Robinson
1983 Automation of Reasoning  
Acknowledgements The authors are deeply indebted to W. F. Miller for his support  ...  The necessity was proved in 1.4 sec., assuming that identity and inverse of the subgroup were that of the group lemmas , just as the presence of a full axiom set, can help or hurt the proof-search.  ...  The lemma states that exponent 3 implies ((a,b),b) = e for all a and b in the group, The proof is shortened considerably (see appendix of [13]) by.the addition of paramodulation to the most  ... 
doi:10.1007/978-3-642-81955-1_33 fatcat:mmo22j33zzbifo6xdx65ym5r2u

The resonance strategy

L. Wos
1995 Computers and Mathematics with Applications  
In contrast, resonators, which capture collections of equations or collections of formulas that may or may not include truths, are used by the resonance strategy to direct the search for the information  ...  Whether the object is to prove a theorem, write an algorithm, or design a circuit, and whether the assignment is given to a person or (preferably) to an automated reasoning program, the judicious use of  ...  He had used OTTER in an impressively successful search for single axioms for groups and for varieties of groups [13] .  ... 
doi:10.1016/0898-1221(94)00220-f fatcat:la2kd5dadzcirhlcckl52zzfvy

Automated Analysis of Diffie-Hellman Protocols and Advanced Security Properties

Benedikt Schmidt, Simon Meier, Cas Cremers, David Basin
2012 2012 IEEE 25th Computer Security Foundations Symposium  
For example, the algorithm successfully verifies the NAXOS protocol with respect to a symbolic version of the eCK security model.  ...  We present a general approach for the symbolic analysis of security protocols that use Diffie-Hellman exponentiation to achieve advanced security properties.  ...  It consists of equations for decryption and projection (1-3), exponentiation (9) (10) , and the theory of abelian groups for the exponents (4) (5) (6) (7) (8) .  ... 
doi:10.1109/csf.2012.25 dblp:conf/csfw/SchmidtMCB12 fatcat:uh5wphwlebbsvagnitzpywgple

A Formal Ontology Reasoning with Individual Optimization: A Realization of the Semantic Web [chapter]

Pakornpong Pothipruk, Guido Governatori
2005 Lecture Notes in Computer Science  
Answering a query over a group of RDF data pages is a trivial process. However, in the Semantic Web, there is a need for ontology technology.  ...  This work demonstrates the techniques for instance checking and instance retrieval problems with respect to ALC description logic which covers certain parts of OWL.  ...  Acknowledgements This work was partially supported by the University of Queensland Early Career Researcher Grant no. 2004001458 on "A System for Automated Agent Negotiation with Defeasible Logic-Based  ... 
doi:10.1007/11581062_10 fatcat:g53otfa6nvdcxc3irnnvxgy2x4
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