4,533 research outputs found
Lower Bounds for Complementation of omega-Automata Via the Full Automata Technique
In this paper, we first introduce a lower bound technique for the state
complexity of transformations of automata. Namely we suggest first considering
the class of full automata in lower bound analysis, and later reducing the size
of the large alphabet via alphabet substitutions. Then we apply such technique
to the complementation of nondeterministic \omega-automata, and obtain several
lower bound results. Particularly, we prove an \omega((0.76n)^n) lower bound
for B\"uchi complementation, which also holds for almost every complementation
or determinization transformation of nondeterministic omega-automata, and prove
an optimal (\omega(nk))^n lower bound for the complementation of generalized
B\"uchi automata, which holds for Streett automata as well
Exploiting the Temporal Logic Hierarchy and the Non-Confluence Property for Efficient LTL Synthesis
The classic approaches to synthesize a reactive system from a linear temporal
logic (LTL) specification first translate the given LTL formula to an
equivalent omega-automaton and then compute a winning strategy for the
corresponding omega-regular game. To this end, the obtained omega-automata have
to be (pseudo)-determinized where typically a variant of Safra's
determinization procedure is used. In this paper, we show that this
determinization step can be significantly improved for tool implementations by
replacing Safra's determinization by simpler determinization procedures. In
particular, we exploit (1) the temporal logic hierarchy that corresponds to the
well-known automata hierarchy consisting of safety, liveness, Buechi, and
co-Buechi automata as well as their boolean closures, (2) the non-confluence
property of omega-automata that result from certain translations of LTL
formulas, and (3) symbolic implementations of determinization procedures for
the Rabin-Scott and the Miyano-Hayashi breakpoint construction. In particular,
we present convincing experimental results that demonstrate the practical
applicability of our new synthesis procedure
Finitary languages
The class of omega-regular languages provides a robust specification language
in verification. Every omega-regular condition can be decomposed into a safety
part and a liveness part. The liveness part ensures that something good happens
"eventually". Finitary liveness was proposed by Alur and Henzinger as a
stronger formulation of liveness. It requires that there exists an unknown,
fixed bound b such that something good happens within b transitions. In this
work we consider automata with finitary acceptance conditions defined by
finitary Buchi, parity and Streett languages. We study languages expressible by
such automata: we give their topological complexity and present a
regular-expression characterization. We compare the expressive power of
finitary automata and give optimal algorithms for classical decisions
questions. We show that the finitary languages are Sigma 2-complete; we present
a complete picture of the expressive power of various classes of automata with
finitary and infinitary acceptance conditions; we show that the languages
defined by finitary parity automata exactly characterize the star-free fragment
of omega B-regular languages; and we show that emptiness is NLOGSPACE-complete
and universality as well as language inclusion are PSPACE-complete for finitary
parity and Streett automata
Can Nondeterminism Help Complementation?
Complementation and determinization are two fundamental notions in automata
theory. The close relationship between the two has been well observed in the
literature. In the case of nondeterministic finite automata on finite words
(NFA), complementation and determinization have the same state complexity,
namely Theta(2^n) where n is the state size. The same similarity between
determinization and complementation was found for Buchi automata, where both
operations were shown to have 2^\Theta(n lg n) state complexity. An intriguing
question is whether there exists a type of omega-automata whose determinization
is considerably harder than its complementation. In this paper, we show that
for all common types of omega-automata, the determinization problem has the
same state complexity as the corresponding complementation problem at the
granularity of 2^\Theta(.).Comment: In Proceedings GandALF 2012, arXiv:1210.202
Good-for-games -Pushdown Automata
We introduce good-for-games -pushdown automata (-GFG-PDA).
These are automata whose nondeterminism can be resolved based on the input
processed so far. Good-for-gameness enables automata to be composed with games,
trees, and other automata, applications which otherwise require deterministic
automata. Our main results are that -GFG-PDA are more expressive than
deterministic - pushdown automata and that solving infinite games with
winning conditions specified by -GFG-PDA is EXPTIME-complete. Thus, we
have identified a new class of -contextfree winning conditions for
which solving games is decidable. It follows that the universality problem for
-GFG-PDA is in EXPTIME as well. Moreover, we study closure properties
of the class of languages recognized by -GFG- PDA and decidability of
good-for-gameness of -pushdown automata and languages. Finally, we
compare -GFG-PDA to -visibly PDA, study the resources necessary
to resolve the nondeterminism in -GFG-PDA, and prove that the parity
index hierarchy for -GFG-PDA is infinite.Comment: Extended version of LICS'20 paper of the same name (DOI
10.1145/3373718.3394737); accepted for publication to LMC
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