Vacuity Checking in the Modal Mu-Calculus*
Identifieur interne : 008722 ( Main/Exploration ); précédent : 008721; suivant : 008723Vacuity Checking in the Modal Mu-Calculus*
Auteurs : Yifei Dong [États-Unis] ; Beata Sarna-Starosta [États-Unis] ; C. R. Ramakrishnan [États-Unis] ; Scott A. Smolka [États-Unis]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: Vacuity arises when a logical formula is trivially true in a given model due, for example, to antecedent failure. Beer et al. have recently introduced a logic-independent notion of vacuity and shown that certain logics, i.e., those with polarity, admit an efficient decision procedure for vacuity detection. We show that the modal mu-calculus, a very expressive temporal logic, is a logic with polarity and hence the results of Beer et al. are applicable. We also extend the definition of vacuity to achieve a new notion of redundancy in logical formulas. Redundancy captures several forms of antecedent failure that escape traditional vacuity analysis, including vacuous actions in temporal modalities and unnecessarily strong temporal operators. Furthermore, we have implemented an efficient redundancy checker for the modal mu-calculus in the context of the XMC model checker. Our checker generates diagnostic information in the form of all maximal subformulas that are redundant and exploits the fact that XMC can cache intermediate results in memo tables between model-checking runs. We have applied our redundancy checker to a number of previously published case studies, and found instances of redundancy that have gone unnoticed till now. These findings provide compelling evidence of the importance of redundancy detection in the design process.
Url:
DOI: 10.1007/3-540-45719-4_11
Affiliations:
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Smolka</name><affiliation wicri:level="2"><country xml:lang="fr">États-Unis</country><wicri:regionArea>Department of Computer Science, State University of New York at Stony Brook, 11794-4400, Stony Brook, NY</wicri:regionArea><placeName><region type="state">État de New York</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">États-Unis</country></affiliation></author></analytic><monogr></monogr><series><title level="s" type="main" xml:lang="en">Lecture Notes in Computer Science</title><idno type="ISSN">0302-9743</idno><idno type="ISSN">0302-9743</idno></series></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: Vacuity arises when a logical formula is trivially true in a given model due, for example, to antecedent failure. Beer et al. have recently introduced a logic-independent notion of vacuity and shown that certain logics, i.e., those with polarity, admit an efficient decision procedure for vacuity detection. We show that the modal mu-calculus, a very expressive temporal logic, is a logic with polarity and hence the results of Beer et al. are applicable. We also extend the definition of vacuity to achieve a new notion of redundancy in logical formulas. Redundancy captures several forms of antecedent failure that escape traditional vacuity analysis, including vacuous actions in temporal modalities and unnecessarily strong temporal operators. Furthermore, we have implemented an efficient redundancy checker for the modal mu-calculus in the context of the XMC model checker. Our checker generates diagnostic information in the form of all maximal subformulas that are redundant and exploits the fact that XMC can cache intermediate results in memo tables between model-checking runs. We have applied our redundancy checker to a number of previously published case studies, and found instances of redundancy that have gone unnoticed till now. These findings provide compelling evidence of the importance of redundancy detection in the design process.</div></front></TEI><affiliations><list><country><li>États-Unis</li></country><region><li>État de New York</li></region></list><tree><country name="États-Unis"><region name="État de New York"><name sortKey="Dong, Yifei" sort="Dong, Yifei" uniqKey="Dong Y" first="Yifei" last="Dong">Yifei Dong</name></region><name sortKey="Dong, Yifei" sort="Dong, Yifei" uniqKey="Dong Y" first="Yifei" last="Dong">Yifei Dong</name><name sortKey="Ramakrishnan, C R" sort="Ramakrishnan, C R" uniqKey="Ramakrishnan C" first="C. R." last="Ramakrishnan">C. R. Ramakrishnan</name><name sortKey="Ramakrishnan, C R" sort="Ramakrishnan, C R" uniqKey="Ramakrishnan C" first="C. R." last="Ramakrishnan">C. R. Ramakrishnan</name><name sortKey="Sarna Starosta, Beata" sort="Sarna Starosta, Beata" uniqKey="Sarna Starosta B" first="Beata" last="Sarna-Starosta">Beata Sarna-Starosta</name><name sortKey="Sarna Starosta, Beata" sort="Sarna Starosta, Beata" uniqKey="Sarna Starosta B" first="Beata" last="Sarna-Starosta">Beata Sarna-Starosta</name><name sortKey="Smolka, Scott A" sort="Smolka, Scott A" uniqKey="Smolka S" first="Scott A." last="Smolka">Scott A. Smolka</name><name sortKey="Smolka, Scott A" sort="Smolka, Scott A" uniqKey="Smolka S" first="Scott A." last="Smolka">Scott A. Smolka</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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