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

*
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*. ...

##
###
SINGLE AXIOMS: WITH AND WITHOUT COMPUTERS

2000
*
Computer Mathematics
*

A shortest

doi:10.1142/9789812791962_0013
fatcat:6iambqypgra5do3kwmfctilawa
*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. ...##
###
The Legacy of a Great Researcher
[chapter]

2013
*
Lecture Notes in Computer Science
*

This article presents examples

doi:10.1007/978-3-642-36675-8_1
fatcat:6nhkdcslprhkbl6ciehihqorwq
*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 ...##
###
The shortest single axioms for groups of exponent 4

1995
*
Computers and Mathematics with Applications
*

We study equations

doi:10.1016/0898-1221(94)00212-4
fatcat:jzv3guc24zf55ebmeu6nkgwio4
*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 ...##
###
Single identities for ternary Boolean algebras

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 ...

##
###
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

1999
*
The AI Magazine
*

In this article,

doi:10.1609/aimag.v20i1.1442
dblp:journals/aim/Loveland99
fatcat:quvjcbyot5fzfga27lzwp6pqwa
*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 ...##
###
The Flowering of Automated Reasoning
[chapter]

2005
*
Lecture Notes in Computer Science
*

This article celebrates with obvious joy

doi:10.1007/978-3-540-32254-2_13
fatcat:p5hhow7whnevtfjmw4imhoakm4
*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). ...##
###
The Mechanization of Mathematics
[chapter]

2004
*
Alan Turing: Life and Legacy of a Great Thinker
*

Turing showed that a complete reduction

doi:10.1007/978-3-662-05642-4_5
fatcat:uwbuvf4bebf7dlvo55l75hd2km
*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. ...##
###
Mechanization of Mathematics

1950
*
Nature
*

Turing showed that a complete reduction

doi:10.1038/1661087a0
fatcat:67maf3rrvjg73mivang5isihza
*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. ...##
###
Automated Verification of Group Key Agreement Protocols

2014
*
2014 IEEE Symposium on Security and Privacy
*

We automatically verify a set

doi:10.1109/sp.2014.19
dblp:conf/sp/SchmidtSCB14
fatcat:t5c3nd2mifcirbrd3rnmhqt32a
*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 ...##
###
Maximal Models and Refutation Completeness: Semidecision Procedures in Automatic Theorem Proving
[chapter]

1983
*
Automation of Reasoning
*

Acknowledgements

doi:10.1007/978-3-642-81955-1_33
fatcat:mmo22j33zzbifo6xdx65ym5r2u
*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 ...##
###
The resonance strategy

1995
*
Computers and Mathematics with Applications
*

In contrast, resonators, which capture collections

doi:10.1016/0898-1221(94)00220-f
fatcat:la2kd5dadzcirhlcckl52zzfvy
*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] . ...##
###
Automated Analysis of Diffie-Hellman Protocols and Advanced Security Properties

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) . ...

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

2005
*
Lecture Notes in Computer Science
*

Answering a query over a

doi:10.1007/11581062_10
fatcat:g53otfa6nvdcxc3irnnvxgy2x4
*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 ...
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