1,039 research outputs found
On Minimization and Learning of Deterministic -Automata in the Presence of Don't Care Words
We study minimization problems for deterministic -automata in the
presence of don't care words. We prove that the number of priorities in
deterministic parity automata can be efficiently minimized under an arbitrary
set of don't care words. We derive that from a more general result from which
one also obtains an efficient minimization algorithm for deterministic parity
automata with informative right-congruence (without don't care words).
We then analyze languages of don't care words with a trivial
right-congruence. For such sets of don't care words it is known that weak
deterministic B\"uchi automata (WDBA) have a unique minimal automaton that can
be efficiently computed from a given WDBA (Eisinger, Klaedtke 2006). We give a
congruence-based characterization of the corresponding minimal WDBA, and show
that the don't care minimization results for WDBA do not extend to
deterministic -automata with informative right-congruence: for this
class there is no unique minimal automaton for a given don't care set with
trivial right congruence, and the minimization problem is NP-hard. Finally, we
extend an active learning algorithm for WDBA (Maler, Pnueli 1995) to the
setting with an additional set of don't care words with trivial
right-congruence.Comment: Version 2 is a minor revision with a few references added, some
additional explanations, and a few typos corrected Version 3: Added "On" to
title, and added a reference for Corollary 4.
Constructing Deterministic ?-Automata from Examples by an Extension of the RPNI Algorithm
The RPNI algorithm (Oncina, Garcia 1992) constructs deterministic finite automata from finite sets of negative and positive example words. We propose and analyze an extension of this algorithm to deterministic ?-automata with different types of acceptance conditions. In order to obtain this generalization of RPNI, we develop algorithms for the standard acceptance conditions of ?-automata that check for a given set of example words and a deterministic transition system, whether these example words can be accepted in the transition system with a corresponding acceptance condition. Based on these algorithms, we can define the extension of RPNI to infinite words. We prove that it can learn all deterministic ?-automata with an informative right congruence in the limit with polynomial time and data. We also show that the algorithm, while it can learn some automata that do not have an informative right congruence, cannot learn deterministic ?-automata for all regular ?-languages in the limit. Finally, we also prove that active learning with membership and equivalence queries is not easier for automata with an informative right congruence than for general deterministic ?-automata
Characterizing Omega-Regularity Through Finite-Memory Determinacy of Games on Infinite Graphs
We consider zero-sum games on infinite graphs, with objectives specified as sets of infinite words over some alphabet of colors. A well-studied class of objectives is the one of ?-regular objectives, due to its relation to many natural problems in theoretical computer science. We focus on the strategy complexity question: given an objective, how much memory does each player require to play as well as possible? A classical result is that finite-memory strategies suffice for both players when the objective is ?-regular. We show a reciprocal of that statement: when both players can play optimally with a chromatic finite-memory structure (i.e., whose updates can only observe colors) in all infinite game graphs, then the objective must be ?-regular. This provides a game-theoretic characterization of ?-regular objectives, and this characterization can help in obtaining memory bounds. Moreover, a by-product of our characterization is a new one-to-two-player lift: to show that chromatic finite-memory structures suffice to play optimally in two-player games on infinite graphs, it suffices to show it in the simpler case of one-player games on infinite graphs. We illustrate our results with the family of discounted-sum objectives, for which ?-regularity depends on the value of some parameters
Polynomial Identification of omega-Automata
We study identification in the limit using polynomial time and data for
models of omega-automata. On the negative side we show that non-deterministic
omega-automata (of types Buchi, coBuchi, Parity, Rabin, Street, or Muller)
cannot be polynomially learned in the limit. On the positive side we show that
the omega-language classes IB, IC, IP, IR, IS, and IM, which are defined by
deterministic Buchi, coBuchi, Parity, Rabin, Streett, and Muller acceptors that
are isomorphic to their right-congruence automata, are identifiable in the
limit using polynomial time and data.
We give polynomial time inclusion and equivalence algorithms for
deterministic Buchi, coBuchi, Parity, Rabin, Streett, and Muller acceptors,
which are used to show that the characteristic samples for IB, IC, IP, IR, IS,
and IM can be constructed in polynomial time.
We also provide polynomial time algorithms to test whether a given
deterministic automaton of type X (for X in {B, C, P, R, S, M})is in the class
IX (i.e. recognizes a language that has a deterministic automaton that is
isomorphic to its right congruence automaton).Comment: This is an extended version of a paper with the same name that
appeared in TACAS2
A Colorful and Robust Measure for FDFAs
We define a measure on families of DFAs (FDFAs) that we show to be robust in
the sense that two FDFAs for the same language are guaranteed to agree on this
measure. This measure tightly relates to the Wagner-Hierarchy (that defines the
complexity of omega regular languages). Inspired by the recently introduced
natural colors of infinite words, we define natural colors for finite words
(prefixes of periods of infinite words). From this semantic definition we
derive the Colorful FDFA a novel canonical model for -regular languages
that also assigns correct colors for finite and infinite words. From the
colorful FDFA, for languages that can be recognized by deterministic B\"uchi or
coB\"uchi automata, we generate a canonical DBA or DCA termed the Black
White Automaton, thus complementing the recent result on canonical good for
games coB\"uchi automata for coB\"uchi languages
Checking NFA equivalence with bisimulations up to congruence
16pInternational audienceWe introduce bisimulation up to congruence as a technique for proving language equivalence of non-deterministic finite automata. Exploiting this technique, we devise an optimisation of the classical algorithm by Hopcroft and Karp. We compare our algorithm to the recently introduced antichain algorithms, by analysing and relating the two underlying coinductive proof methods. We give concrete examples where we exponentially improve over antichains; experimental results moreover show non negligible improvements on random automata
A novel family of finite automata for recognizing and learning -regular languages
Families of DFAs (FDFAs) have recently been introduced as a new
representation of -regular languages. They target ultimately periodic
words, with acceptors revolving around accepting some representation . Three canonical FDFAs have been suggested, called periodic,
syntactic, and recurrent. We propose a fourth one, limit FDFAs, which can be
exponentially coarser than periodic FDFAs and are more succinct than syntactic
FDFAs, while they are incomparable (and dual to) recurrent FDFAs. We show that
limit FDFAs can be easily used to check not only whether {\omega}-languages are
regular, but also whether they are accepted by deterministic B\"uchi automata.
We also show that canonical forms can be left behind in applications: the limit
and recurrent FDFAs can complement each other nicely, and it may be a good way
forward to use a combination of both. Using this observation as a starting
point, we explore making more efficient use of Myhill-Nerode's right
congruences in aggressively increasing the number of don't-care cases in order
to obtain smaller progress automata. In pursuit of this goal, we gain
succinctness, but pay a high price by losing constructiveness
- …