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	Büchi automaton - Wikipedia, the free encyclopedia
		A Büchi automaton is the extension of a finite state automaton to infinite inputs.
		It accepts an infinite input sequence, iff there exists a run of the automaton (in case of a deterministic automaton, there is exactly one possible run) which has infinitely many states in the set of final states.
		A language defined by a Rabin automaton, Streett automaton, parity automaton, or Muller automaton is also omega-regular.
	en.wikipedia.org /wiki/B%C3%BCchi_automaton (360 words)

	HOL and PSL2CTL (Version 1.22)
		A Büchi automaton looks exactly like a finite automaton, except that instead of final states, the set F is interpreted as accepting states, and a run is accepted iff some accepting state appears infinitely often in the infinite word being examined.
		The point is that translating the Kripke structure into an automaton, as they are doing in section 9.2, is for the purpose of creating the cross-product of the automaton for the model and the automaton for the formula being checked.
		You want words to be rejected by the resulting automaton because of the automaton of the formula, not the automaton of the Kripke structure, therefore, you make all states in the automaton of the Kripke structure accepting states.
	www.cl.cam.ac.uk /~mjcg/PSL/psl2ctl (2344 words)

	The ltl package: files
		Return a array of all the inputnames of the automaton.
		Minimize the Automaton using I/O Compatiblility and Dominance.
		Return 1 iff the following statement in the automaton holds: For each fair set, if 'state' is in it, 'otherstate' must also in it.
	vlsi.colorado.edu /~vis/doc/html/ltlAllFile.html (910 words)

	Test round messages - `lbtt'
		Information about the Büchi automaton that `Implementation 0' generated from the positive LTL formula (number of states, transitions and acceptance conditions, and the amount of user time elapsed in generating the automaton).
		In this case, the automaton cannot reach an “accepting cycle” regardless of the state of the state space in which the automaton could begin its execution.
		Note that the Büchi automata intersection emptiness check may fail on the automata constructed by the same implementation; in the following example, the check failed between the automata constructed by `Implementation 0', and the automata constructed by `Implementation 0' and `Implementation 1' from the positive and negative formulas, respectively.
	www.tcs.hut.fi /Software/lbtt/doc/html/Test-round-messages.html (732 words)

	CIAA 2005 - Abstracts
		We shall classify the methods that build an automaton from an expression and present with more details the one which is probably the lesser known: Antimirov's construction of derived term automaton.
		An automaton is characterized by properties of its underlying digraph.
		A recursive automaton can be considered as a special case of a recursive transition network, but reduced to one single automaton.
	www.i3s.unice.fr /ciaa05/abstracts.html (4553 words)

	Olivier Finkel
		In particular, we show that one cannot decide whether a given timed automaton is determinizable or whether the complement of a timed regular language is timed regular.
		In the case of a function F accepted by a synchronous 2-tape Büchi automaton we show that the set C(F) is an omega regular set which can be computed.
		This result cannot be extended to the case of asynchronous omega rational functions: one cannot decide whether the set C(F) of an omega rational function F is empty, rational, or context free.
	www.logique.jussieu.fr /www.finkel (4514 words)

	Selected publications by Paul Gastin (Site not responding. Last check: 2007-10-23)
		This algorithm generates a very weak alternating automaton and then transforms it into a Büchi automaton, using a generalized Büchi automaton as an intermediate step.
		Each automaton is simplified on-the-fly in order to save memory and time.
		The criteria of comparison are the size of the resulting automaton, the time of the computation and the memory used.
	www.lsv.ens-cachan.fr /~gastin/mes-publis.php?onlykey=GaOd01 (149 words)

	Metatheory in the standard sense (Site not responding. Last check: 2007-10-23)
		Figure 1 shows a Büchi automaton for a certain language (specified in the caption).
		The key idea in moving from formulas of linear time temporal logic to their corresponding Büchi automata is that such formulas can be viewed as true on certain infinite histories.
		In this flow graph, acceptance happens only if the accept state (the double circle) is ``hit'' infinitely many times.
	www.rpi.edu /~brings/LOG+AI/lai/node12.html (622 words)

	Automated Verification: Assignment 5 (Site not responding. Last check: 2007-10-23)
		Show that for each n there is a PLTL formula of length O(n) such that if A is a Büchi automaton that accepts precisely models(phi), then A has at least 2
		Prove by reduction from the space-bounded tiling problem that satisfiabilty, validity, and model checking for PLTL are PSPACE-hard.
		) be a nondeterministic automaton where rho'(T,A)={T' : T' satisfies rho(t,a) for all t in T}.
	www.wisdom.weizmann.ac.il /~verify/courses/av99/assignments/assign5.html (78 words)

	Ongoing / Current Researches
		By simultaneous exploitation of symmetries of both the system and the property, the model checking can be performed on a reduced quotient structure [2,6,7].
		In these techniques a property is specified within a temporal logic formula (CTL) and symmetries correspond to permutations of objects which are obtained by either a syntactical checking [7] or semantical one through the state of the corresponding automaton* [6].
		Such symmetries are detected within the Büchi automaton of the formula and form a set of symmetries even if the fomula is not globally symmetrical i.e.
	www.lip6.fr /en/production/publications-rapport-fiche.php?RECORD_KEY(rapports)=id&id(rapports)=60 (215 words)

	Automated Verification: Assignment 7 (Site not responding. Last check: 2007-10-23)
		Show that an alternating Büchi automaton (ABW) has an accepting run iff it has a run in which infinitely many levels have finite rank.
		Show that an alternating Büchi automaton has an accepting tree run iff it has an accepting dag run.
		Compare it to the nondeterministic automaton that you will get, using the Miyano-Hayashi translation, from the alternating Büchi automaton defined in class for this formula.
	www.wisdom.weizmann.ac.il /~vardi/av/assignments/assign7.html (148 words)

	Model checking is refinement - Relating Buechi testing and linear-time temporal logic - (Site not responding. Last check: 2007-10-23)
		Using Buechi automata as a semantic basis, the paper introduces two refinement preorders based on DeNicola and Hennessy's notion of may- and must-testing.
		More precisely, it is shown that a labeled transition system satisfies an LTL formula if and only if it refines an appropriately defined Buechi automaton that can be constructed from the formula.
		The implications of the novel theory are illustrated by means of a simple example system, in which some components are specified as transition systems and others as LTL formulas.
	www.icase.edu /library/reports/rdp/2000/2000-14RDP.tex.refer.html (236 words)

	Automata Generation for On-the-fly Automatic Verification Using Formulas of an Interval Logic (Site not responding. Last check: 2007-10-23)
		An algorithm is developed to construct a Büchi automaton which is semantically equivalent to system specification described by means of FIL formulas.
		The algorithm is intended to be used within the framework of on-the-fly model checking methods as way of solving the problem of verifying reactive systems.
		The algorithm uses these rules to reduce a formula into simpler ones, which are satisfied by the states of the automaton run.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/acsd/2001/1071/00/1071toc.xml&DOI=10.1109/CSD.2001.981779 (222 words)

	Math 670 Fall 1998 MWF 10:30-12 DRL 4C4
		Finish the proof that the construction given in class of the alternating Büchi automaton associated to a given temporal formula has the desired property that the automaton accepts an infinite word iff this word when considered as a temporal model satisfies the formula.
		In each case prove in detail that the infinitary language of the alternating Büchi automaton is precisely the set of linear temporal logic models satisfying the formula.
		Prove in detail PSPACE-hardness of the satisfiablity problem for linear temporal logic by describing a logarithmic-space algorithm that given a PSPACE-bounded Turing machine M and a finite word w outputs a linear temporal logic formula such that the formula is satisfiable iff M accepts w.
	www.cis.upenn.edu /~scedrov/courses/Math670F98.html (458 words)

	NFA or DFA? [Theory] (Site not responding. Last check: 2007-10-23)
		"eventually always a", which cannot be expressed by a deterministic Buechi
		automaton, because the automaton has to see "into the future" to recognize
		indeed recognize the omega-languages, whereas the deterministic Buechi
	www.adras.com /NFA-or-DFA.t35-57-1.html (306 words)

	Promela Reference -- never(2)
		The following is achieved by having the verifier compute a synchronous (instead of an asynchronous) product of the sequence specified in the temporal claim, with the interleaving sequences specified in the remainder of the system.
		This synchronous product can be thought of as the construction of a new automaton, in which every state is defined as a pair
		Every transition in the new automaton is similarly defined by a pair of transitions, with the first element a statement from the system, and the second a proposition from the claim.
	www.cse.msu.edu /~cse470/PromelaManual/never.html (984 words)

	INI : Abstracts : LAA : Solving Games without Determinization (Site not responding. Last check: 2007-10-23)
		When the objective is specified by a linear temporal logic formula or nondeterministic Buechi automaton, then previous algorithms for solving the game require the construction of an equivalent deterministic automaton.
		However, determinization for automata on infinite words is extremely complicated, and current implementations fail to produce deterministic automata even for relatively small inputs.
		We show how to construct, from a given nondeterministic Buechi automaton, an equivalent nondeterministic parity automaton N that is good for solving games with objective N. The main insight is that a nondeterministic automaton is good for solving games if it fairly simulates the equivalent deterministic automaton.
	www.newton.cam.ac.uk /programmes/LAA/piterman.html (163 words)

	Computing Reviews, the leading online review service for computing literature. (Site not responding. Last check: 2007-10-23)
		The first part introduces alternating Büchi automata, and sketches a proof of the result: that an alternating Büchi automaton is equivalent to a certain formula of mu-calculus.
		The nondeterministic variant of the alternating Büchi automata is described in the second part, and it is shown that every tree language accepted by an alternating Büchi automaton is accepted by a nondeterministic Büchi automaton.
		The last part defines a weak variant of alternating Büchi automata, and proves via a simulation theorem that alternating weak Büchi automata are equivalent to nondeterministic Büchi automata.
	www.reviews.com /review/review_review.cfm?review_id=131977&listname=highlight (640 words)

	TGBA - Spot Wiki
		TGBA stands for for Transition-based Generalized Büchi Automaton.
		Also it uses generalized acceptance conditions, meaning there are several sets of transitions.
		A path in the automaton is accepted if it passes infinitely often by one transition of each acceptance set.
	spot.lip6.fr /wiki/TGBA (318 words)

	Python: module BuechiAutomaton (Site not responding. Last check: 2007-10-23)
		Save this Buechi automaton in the given format.
		Save the automaton in the format of a Promela never-claim.
		Write the automaton in the format of a Promela never-claim.We assume that the transitionRelation is in the format Dict of (state, Dict of (state, list of term)).
	www.ti.informatik.uni-kiel.de /~teegen/ABA-Simulation/api/BuechiAutomaton.html (168 words)

	Information and Computation Bibliography (Site not responding. Last check: 2007-10-23)
		The condition requiered of the set \Gamma there, is that the intersection with natural numbers forms a recognizable set.
		Finally, we exhibit a set of trees which is recognized by a classical Büchi automaton but fails to be recognized by any Muller automaton with a non trivial cardinality constraint (i.e., except for \Gamma = 0).
		The abstract is also available as a LaTeX file, a DVI file, or a PostScript file.
	theory.lcs.mit.edu /~iandc/References/beauquiern1995:117.html (240 words)

	CSAIL Event Calendar
		We present mc^2, what we believe to be the first randomized, Monte Carlo algorithm for temporal-logic model checking, the classical problem of deciding whether or not a property specified in temporal logic holds of a system specification.
		Given a specification $S$ of a finite-state system, an LTL (Linear Temporal Logic) formula $\varphi$, and parameters $\epsilon$ and $\delta$, mc^2 takes $N=\ln(\delta)/\ln(1-\epsilon)$ random samples (random walks ending in a cycle, i.e lassos) from the Buechi automaton $B=B_S \times B_{\neg\varphi}$ to decide if $L(B)=\emptyset$.
		Should a sample reveal an accepting lasso $l$, mc^2 returns false with $l$ as a witness.
	www.csail.mit.edu /events/eventcalendar/calendar.php?show=event&id=475 (210 words)

	Model Checking UML Statecharts (Site not responding. Last check: 2007-10-23)
		Then, the way of how UML statecharts is structurally expressed by extended hierarchical automaton and the labeled transition system are defined.
		The correctness of operational semantics of UML statecharts can be ensured through finding the maximal non-conflict transition set.
		For the system with infinite runs, the operational semantics can be mapped to a Büchi automaton and linear temporal logic properties of the system can be verified based on the automata theory of model checking.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/apsec/2001/1408/00/1408toc.xml&DOI=10.1109/APSEC.2001.991503 (218 words)

	On the Complexity of Parity Word Automata - King, Kupferman, Vardi (ResearchIndex) (Site not responding. Last check: 2007-10-23)
		A simple translation of a parity automaton to an equivalent Büchi automaton is quadratic: a parity automaton with n states, m transitions, and index k may result in a Büchi automaton of size O((n + m)k).
		The best known algorithm for the nonemptiness problem of parity automata goes through Büchi automata, leading to a complexity of O((n + m)k).
		...to be solvable in time O(n m)d) for an automaton with n states, m transitions and d even priorities.
	citeseer.ist.psu.edu /king01complexity.html (595 words)

	[No title]
		Empty?¡:4(2 ª 4 ð¢ ðd ð0ãá¿¿Àÿð/IÃ ð²¨nDuplicate automaton.
		When leaving an accept state, jump to next automaton.
		In order for the language to be non-empty, there must be an infinite run of the automaton that visits an accept state infinitely often.
	www.daimi.au.dk /Conver/ltl-model-checking-final.ppt (705 words)

	LTL2BA4J - Java bridge to ltl2ba
		This is much faster, since all the data conversion is directly handled in the virtual machine.
		As we found out, Java Pathfinder provides a LTL to Büchi automaton conversion engine as well.
		This is written in pure Java and provides the following two algorithms:
	www-i2.informatik.rwth-aachen.de /Forschung/RV/ltl2ba4j (443 words)

	LTL model checking
		, since we need it to build the Büchi automaton
		in the hope of generating a smaller Büchi automaton
		This module is optional (the user may choose to include it or not when doing model checking) but tends to help building a smaller
	maude.cs.uiuc.edu /maude2-manual/html/node119.html (1659 words)

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