Knuth–Bendix completion of theories of commuting group endomorphisms
Knuth–Bendix completions of the equational theories of k ⩾ 2 commuting group endomorphisms are obtained, using automated theorem proving and modern termination checking. This improves on modern implementations of completion, where the orderings implemented cannot orient the commutation rules. The re...
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| Published in | Information processing letters Vol. 98; no. 5; pp. 195 - 198 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier B.V
15.06.2006
Elsevier Science Elsevier Sequoia S.A |
| Subjects | |
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| Abstract | Knuth–Bendix completions of the equational theories of
k
⩾
2
commuting group endomorphisms are obtained, using automated theorem proving and modern termination checking. This improves on modern implementations of completion, where the orderings implemented cannot orient the commutation rules. The result has applications in decision procedures for automated verification. |
|---|---|
| AbstractList | Knuth–Bendix completions of the equational theories of
k
⩾
2
commuting group endomorphisms are obtained, using automated theorem proving and modern termination checking. This improves on modern implementations of completion, where the orderings implemented cannot orient the commutation rules. The result has applications in decision procedures for automated verification. Knuth-Bendix completions of the equational theories of k > 2 commuting group endomorphisms are obtained, using automated theorem proving and modern termination checking. This improves on modern implementations of completion, where the orderings implemented cannot orient the commutation rules. The result has applications in decision procedures for automated verification. Decision procedures for first-order theories like fragments of arithmetic or theories of arrays are the subject of current intensive study for their applications in automated verification. Modern decision procedures for satisfiability modulo such theories are built by combining techniques for fast propositional reasoning with theory specific reasoners. It has been empirically established that a tight interaction between the theory reasoner and the propositional reasoner is critical for high performance. One point of interaction occurs when the theory reasoner detects that the assignment chosen by the propositional reasoner is inconsistent modulo the background theory. In this case, the theory solver should identify as small a subset as possible of the current assignment which is still inconsistent. |
| Author | Stump, Aaron Löchner, Bernd |
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| Keywords | Knuth–Bendix completion Decision procedures Automatic theorem proving Group theory Knuth Bendix completion Computer theory Theorem proving Ordering Automatic proving Verification Knuth-Bendix completion Equational theory |
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| References | Giesl, Arts, Ohlebusch (bib003) 2002; 34 Barrett, Dill, Stump (bib001) 2002 Knuth, Bendix (bib005) 1970 Löchner, Hillenbrand (bib006) 2002; 15 de Moura, Rueß, Shankar (bib002) 2005; 125 Stump, Tan (bib008) 2005 Nieuwenhuis, Oliveras (bib007) 2005 Giesl, Thiemann, Schneider-Kamp, Falke (bib004) 2004 Stump (10.1016/j.ipl.2006.01.009_bib008) 2005 de Moura (10.1016/j.ipl.2006.01.009_bib002) 2005; 125 Knuth (10.1016/j.ipl.2006.01.009_bib005) 1970 Giesl (10.1016/j.ipl.2006.01.009_bib003) 2002; 34 Barrett (10.1016/j.ipl.2006.01.009_bib001) 2002 Löchner (10.1016/j.ipl.2006.01.009_bib006) 2002; 15 Nieuwenhuis (10.1016/j.ipl.2006.01.009_bib007) 2005 Giesl (10.1016/j.ipl.2006.01.009_bib004) 2004 |
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| Snippet | Knuth–Bendix completions of the equational theories of
k
⩾
2
commuting group endomorphisms are obtained, using automated theorem proving and modern termination... Knuth-Bendix completions of the equational theories of k > 2 commuting group endomorphisms are obtained, using automated theorem proving and modern termination... |
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| SubjectTerms | Algorithmics. Computability. Computer arithmetics Applied sciences Automatic theorem proving Automation Computer science; control theory; systems Decision procedures Exact sciences and technology Group theory Group theory and generalizations Knuth–Bendix completion Logic and foundations Mathematical logic, foundations, set theory Mathematical models Mathematics Proof theory and constructive mathematics Sciences and techniques of general use Studies Theoretical computing Theory |
| Title | Knuth–Bendix completion of theories of commuting group endomorphisms |
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