Verification of infinite-state dynamic systems using approximate quotient transition systems
This paper deals with computational methods for verifying properties of labeled infinite-state transition systems using quotient transition system (QTS). A QTS is a conservative approximation to the infinite-state transition system based on a finite partition of the infinite state space. For univers...
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| Veröffentlicht in: | IEEE transactions on automatic control 2001-09, Vol.46 (9), p.1401-1410 |
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| creator | Chutinan, A. Krogh, B.H. |
| description | This paper deals with computational methods for verifying properties of labeled infinite-state transition systems using quotient transition system (QTS). A QTS is a conservative approximation to the infinite-state transition system based on a finite partition of the infinite state space. For universal specifications, positive verification for a QTS implies the specification is true for the infinite-state transition system. We introduce the approximate QTS or AQTS. The paper presents a sufficient condition for an AQTS to be a bisimulation of the infinite state transition system. An AQTS bisimulation is essentially equivalent to the infinite-state system for the purposes of verification. It is well known, however, that finite-state bisimulations do not exist for most hybrid systems of practical interest. Therefore, the use of the AQTS for verification of universal specifications is proposed and illustrated with an example. This approach has been implemented in a tool for computer-aided verification of a general class of hybrid systems. |
| doi_str_mv | 10.1109/9.948467 |
| format | Article |
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A QTS is a conservative approximation to the infinite-state transition system based on a finite partition of the infinite state space. For universal specifications, positive verification for a QTS implies the specification is true for the infinite-state transition system. We introduce the approximate QTS or AQTS. The paper presents a sufficient condition for an AQTS to be a bisimulation of the infinite state transition system. An AQTS bisimulation is essentially equivalent to the infinite-state system for the purposes of verification. It is well known, however, that finite-state bisimulations do not exist for most hybrid systems of practical interest. Therefore, the use of the AQTS for verification of universal specifications is proposed and illustrated with an example. 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A QTS is a conservative approximation to the infinite-state transition system based on a finite partition of the infinite state space. For universal specifications, positive verification for a QTS implies the specification is true for the infinite-state transition system. We introduce the approximate QTS or AQTS. The paper presents a sufficient condition for an AQTS to be a bisimulation of the infinite state transition system. An AQTS bisimulation is essentially equivalent to the infinite-state system for the purposes of verification. It is well known, however, that finite-state bisimulations do not exist for most hybrid systems of practical interest. Therefore, the use of the AQTS for verification of universal specifications is proposed and illustrated with an example. This approach has been implemented in a tool for computer-aided verification of a general class of hybrid systems.</description><subject>Approximation</subject><subject>Dynamical systems</subject><subject>Dynamics</subject><subject>Equivalence</subject><subject>Formal verification</subject><subject>Hybrid systems</subject><subject>Laboratories</subject><subject>Logic</subject><subject>Mathematical analysis</subject><subject>Quotients</subject><subject>Reachability analysis</subject><subject>Specifications</subject><subject>State-space methods</subject><subject>Studies</subject><subject>Sufficient conditions</subject><subject>Tree graphs</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2001</creationdate><recordtype>article</recordtype><sourceid>RIE</sourceid><recordid>eNqN0UtLAzEQAOAgCtYqePa0eFAvW5NsJo-jFF8geFFPwpKmWUnpZtskC_bfmz7w4EFlDsMwH8Mwg9ApwSNCsLpWI8Uk42IPDQiALCnQah8NMCayVFTyQ3QU4yyXnDEyQO9vNrjGGZ1c54uuKZxvnHfJljHpZIvpyuvWmSKuYrJtLPro_EehF4vQfbp2LZZ9l5z1qUhB--g2c3b6GB00eh7tyS4P0evd7cv4oXx6vn8c3zyVhlFIpaGCclFVhguqDEwmFoyRwKsKa2o1V43UYqoMt9BgQQwRDMAABTXlihJTDdHldm7eatnbmOrWRWPnc-1t18daEcZBAaFZXvwqqcKKMpB_Q8mFUP-BAleUcpzh-Q846_rg811qKRkwSdkaXW2RCV2MwTb1IuQzh1VNcL3-b51j899Mz7bUWWu_2a75BYRioAE</recordid><startdate>20010901</startdate><enddate>20010901</enddate><creator>Chutinan, A.</creator><creator>Krogh, B.H.</creator><general>IEEE</general><general>The Institute of Electrical and Electronics Engineers, Inc. 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A QTS is a conservative approximation to the infinite-state transition system based on a finite partition of the infinite state space. For universal specifications, positive verification for a QTS implies the specification is true for the infinite-state transition system. We introduce the approximate QTS or AQTS. The paper presents a sufficient condition for an AQTS to be a bisimulation of the infinite state transition system. An AQTS bisimulation is essentially equivalent to the infinite-state system for the purposes of verification. It is well known, however, that finite-state bisimulations do not exist for most hybrid systems of practical interest. Therefore, the use of the AQTS for verification of universal specifications is proposed and illustrated with an example. 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| source | IEEE Electronic Library (IEL) |
| subjects | Approximation Dynamical systems Dynamics Equivalence Formal verification Hybrid systems Laboratories Logic Mathematical analysis Quotients Reachability analysis Specifications State-space methods Studies Sufficient conditions Tree graphs |
| title | Verification of infinite-state dynamic systems using approximate quotient transition systems |
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