83 research outputs found
Partially Ordered Two-way B\"uchi Automata
We introduce partially ordered two-way B\"uchi automata and characterize
their expressive power in terms of fragments of first-order logic FO[<].
Partially ordered two-way B\"uchi automata are B\"uchi automata which can
change the direction in which the input is processed with the constraint that
whenever a state is left, it is never re-entered again. Nondeterministic
partially ordered two-way B\"uchi automata coincide with the first-order
fragment Sigma2. Our main contribution is that deterministic partially ordered
two-way B\"uchi automata are expressively complete for the first-order fragment
Delta2. As an intermediate step, we show that deterministic partially ordered
two-way B\"uchi automata are effectively closed under Boolean operations.
A small model property yields coNP-completeness of the emptiness problem and
the inclusion problem for deterministic partially ordered two-way B\"uchi
automata.Comment: The results of this paper were presented at CIAA 2010; University of
Stuttgart, Computer Scienc
How Much Lookahead is Needed to Win Infinite Games?
Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent’s moves. For ω-regular winning conditions it is known that such games can be solved in doubly-exponential time and that doubly-exponential lookahead is sufficient. We improve upon both results by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead. This is complemented by showing ExpTime-hardness of the solution problem and tight exponential lower bounds on the lookahead. Both lower bounds already hold for safety conditions. Furthermore, solving delay games with reachability conditions is shown to be PSpace-complete
Delay Games with WMSO+U Winning Conditions
Delay games are two-player games of infinite duration in which one player may
delay her moves to obtain a lookahead on her opponent's moves. We consider
delay games with winning conditions expressed in weak monadic second order
logic with the unbounding quantifier, which is able to express (un)boundedness
properties. We show that it is decidable whether the delaying player has a
winning strategy using bounded lookahead and give a doubly-exponential upper
bound on the necessary lookahead. In contrast, we show that bounded lookahead
is not always sufficient to win such a game.Comment: A short version appears in the proceedings of CSR 2015. The
definition of the equivalence relation introduced in Section 3 is updated:
the previous one was inadequate, which invalidates the proof of Lemma 2. The
correction presented here suffices to prove Lemma 2 and does not affect our
main theorem. arXiv admin note: text overlap with arXiv:1412.370
A Class of Automata for the Verification of Infinite, Resource-Allocating Behaviours
Process calculi for service-oriented computing often feature generation of fresh resources. So-called nominal automata have been studied both as semantic models for such calculi, and as acceptors of languages of finite words over infinite alphabets. In this paper we investi-gate nominal automata that accept infinite words. These automata are a generalisation of deterministic Muller automata to the setting of nominal sets. We prove decidability of complement, union, intersection, emptiness and equivalence, and determinacy by ultimately periodic words. The key to obtain such results is to use finite representations of the (otherwise infinite-state) defined class of automata. The definition of such operations enables model checking of process calculi featuring infinite behaviours, and resource allocation, to be implemented using classical automata-theoretic methods
Component-wise incremental LTL model checking
Efficient symbolic and explicit-state model checking
approaches have been developed for the verification of linear
time temporal
logic (LTL) properties. Several attempts have been made to
combine the advantages of the various algorithms. Model
checking LTL
properties usually poses two challenges: one must compute the
synchronous product of the state space and the automaton
model of the
desired property, then look for counterexamples that is
reduced to finding strongly connected components (SCCs) in
the state space
of the product. In case of concurrent systems, where the
phenomenon of state space explosion often prevents the
successful
verification, the so-called saturation algorithm has proved
its efficiency in state space exploration. This paper
proposes a new
approach that leverages the saturation algorithm both as an
iteration strategy constructing the product directly, as well
as in a
new fixed-point computation algorithm to find strongly
connected components on-the-fly by incrementally processing
the components
of the model. Complementing the search for SCCs, explicit
techniques and component-wise abstractions are used to prove
the absence
of counterexamples. The resulting on-the-fly, incremental LTL
model checking algorithm proved to scale well with the size
of
models, as the evaluation on models of the Model Checking
Contest suggests
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