Control of ω-automata, Church's problem, and the emptiness problem for tree ω-automata
Church's problem and the emptiness problem for Rabin automata on infinite trees, which represent basic paradigms for program synthesis and logical decision procedures, are formulated as a control problem for automata on infinite strings. The alphabet of an automaton is interpreted not as a set...
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| creator | Thistle, J. G. Wonham, W. M. |
| description | Church's problem and the emptiness problem for Rabin automata on infinite trees, which represent basic paradigms for program synthesis and logical decision procedures, are formulated as a control problem for automata on infinite strings. The alphabet of an automaton is interpreted not as a set of input symbols giving rise to state transitions but rather as a set of output symbols generated during spontaneous state transitions; in addition, it is assumed that automata can be “controlled” through the imposition of certain allowable restrictions on the set of symbols that may be generated at a given instant. The problems in question are then recast as that of deciding membership in a deterministic Rabin automaton's controllability subset — the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition. The new formulation leads to a direct, efficient and natural solution based on a fixpoint representation of the controllability subset. This approach combines advantages of earlier solutions and admits useful extensions incorporating liveness assumptions. |
| doi_str_mv | 10.1007/BFb0023782 |
| format | Book Chapter |
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G. ; Wonham, W. M.</creator><contributor>Jäger, Gerhard ; Kleine Büning, Hans ; Richter, Michael M. ; Börger, Egon</contributor><creatorcontrib>Thistle, J. G. ; Wonham, W. M. ; Jäger, Gerhard ; Kleine Büning, Hans ; Richter, Michael M. ; Börger, Egon</creatorcontrib><description>Church's problem and the emptiness problem for Rabin automata on infinite trees, which represent basic paradigms for program synthesis and logical decision procedures, are formulated as a control problem for automata on infinite strings. The alphabet of an automaton is interpreted not as a set of input symbols giving rise to state transitions but rather as a set of output symbols generated during spontaneous state transitions; in addition, it is assumed that automata can be “controlled” through the imposition of certain allowable restrictions on the set of symbols that may be generated at a given instant. 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The problems in question are then recast as that of deciding membership in a deterministic Rabin automaton's controllability subset — the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition. The new formulation leads to a direct, efficient and natural solution based on a fixpoint representation of the controllability subset. This approach combines advantages of earlier solutions and admits useful extensions incorporating liveness assumptions.</description><subject>Acceptance Condition</subject><subject>Infinite Tree</subject><subject>Sequential Calculus</subject><subject>State Subset</subject><subject>Tree Automaton</subject><issn>0302-9743</issn><issn>1611-3349</issn><isbn>354055789X</isbn><isbn>9783540557890</isbn><isbn>3540472851</isbn><isbn>9783540472858</isbn><fulltext>true</fulltext><rsrctype>book_chapter</rsrctype><creationdate>1992</creationdate><recordtype>book_chapter</recordtype><sourceid/><recordid>eNpNkLtOwzAYRs1NopQuPIE3GBrw70vsjBBRQKrEAlK3yG5-00ISV7b7EDwdrwSoCPiWbzjSGQ4hZ8AugTF9dTNzjHGhDd8jJ0JJJjU3CvbJCEqAQghZHeyAUtpUi0MyYoLxotJSHJNJSq_sa4JzEHxEFnUYcgwdDZ5-vBd2m0Nvs53SerWNy9V5opsYXIf9lNqhpXmFFPtNXg-YfhH1IdIcEf8bTsmRt13Cyc-PyfPs9qm-L-aPdw_19bxIYEwuoAXpNHOybUtQXnvtPOfcYskd0woUeoHKKlsab5RdVlgqL9FJXnLWGi3G5GLnTZu4Hl4wNi6Et9QAa75zNX-5xCdPcVlX</recordid><startdate>19920101</startdate><enddate>19920101</enddate><creator>Thistle, J. G.</creator><creator>Wonham, W. M.</creator><general>Springer Berlin Heidelberg</general><scope/></search><sort><creationdate>19920101</creationdate><title>Control of ω-automata, Church's problem, and the emptiness problem for tree ω-automata</title><author>Thistle, J. G. ; Wonham, W. M.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-s188t-1d14b70b4dd615f7f7bf222ae62b07515ef3e5a5a68f85ac9e65f4eb42620d873</frbrgroupid><rsrctype>book_chapters</rsrctype><prefilter>book_chapters</prefilter><language>eng</language><creationdate>1992</creationdate><topic>Acceptance Condition</topic><topic>Infinite Tree</topic><topic>Sequential Calculus</topic><topic>State Subset</topic><topic>Tree Automaton</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Thistle, J. G.</creatorcontrib><creatorcontrib>Wonham, W. M.</creatorcontrib></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Thistle, J. G.</au><au>Wonham, W. M.</au><au>Jäger, Gerhard</au><au>Kleine Büning, Hans</au><au>Richter, Michael M.</au><au>Börger, Egon</au><format>book</format><genre>bookitem</genre><ristype>CHAP</ristype><atitle>Control of ω-automata, Church's problem, and the emptiness problem for tree ω-automata</atitle><btitle>Computer Science Logic</btitle><seriestitle>Lecture Notes in Computer Science</seriestitle><date>1992-01-01</date><risdate>1992</risdate><spage>367</spage><epage>381</epage><pages>367-381</pages><issn>0302-9743</issn><eissn>1611-3349</eissn><isbn>354055789X</isbn><isbn>9783540557890</isbn><eisbn>3540472851</eisbn><eisbn>9783540472858</eisbn><abstract>Church's problem and the emptiness problem for Rabin automata on infinite trees, which represent basic paradigms for program synthesis and logical decision procedures, are formulated as a control problem for automata on infinite strings. The alphabet of an automaton is interpreted not as a set of input symbols giving rise to state transitions but rather as a set of output symbols generated during spontaneous state transitions; in addition, it is assumed that automata can be “controlled” through the imposition of certain allowable restrictions on the set of symbols that may be generated at a given instant. The problems in question are then recast as that of deciding membership in a deterministic Rabin automaton's controllability subset — the set of states from which the automaton can be controlled to the satisfaction of its own acceptance condition. The new formulation leads to a direct, efficient and natural solution based on a fixpoint representation of the controllability subset. This approach combines advantages of earlier solutions and admits useful extensions incorporating liveness assumptions.</abstract><cop>Berlin, Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/BFb0023782</doi><tpages>15</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0302-9743 |
| ispartof | Computer Science Logic, 1992, p.367-381 |
| issn | 0302-9743 1611-3349 |
| language | eng |
| recordid | cdi_springer_books_10_1007_BFb0023782 |
| source | Springer Books |
| subjects | Acceptance Condition Infinite Tree Sequential Calculus State Subset Tree Automaton |
| title | Control of ω-automata, Church's problem, and the emptiness problem for tree ω-automata |
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