33 research outputs found
From Finite Automata to Regular Expressions and Back--A Summary on Descriptional Complexity
The equivalence of finite automata and regular expressions dates back to the
seminal paper of Kleene on events in nerve nets and finite automata from 1956.
In the present paper we tour a fragment of the literature and summarize results
on upper and lower bounds on the conversion of finite automata to regular
expressions and vice versa. We also briefly recall the known bounds for the
removal of spontaneous transitions (epsilon-transitions) on non-epsilon-free
nondeterministic devices. Moreover, we report on recent results on the average
case descriptional complexity bounds for the conversion of regular expressions
to finite automata and brand new developments on the state elimination
algorithm that converts finite automata to regular expressions.Comment: In Proceedings AFL 2014, arXiv:1405.527
Ambiguity, nondeterminism and state complexity of finite automata
The degree of ambiguity counts the number of accepting computations of a nondeterministic finite automaton (NFA) on a given input. Alternatively, the nondeterminism of an NFA can be measured by counting the amount of guessing in a single computation or the number of leaves of the computation tree on a given input. This paper surveys work on the degree of ambiguity and on various nondeterminism measures for finite automata. In particular, we focus on state complexity comparisons between NFAs with quantified ambiguity or nondeterminism
26. Theorietag Automaten und Formale Sprachen 23. Jahrestagung Logik in der Informatik: Tagungsband
Der Theorietag ist die Jahrestagung der Fachgruppe Automaten und Formale Sprachen der Gesellschaft für Informatik und fand erstmals 1991 in Magdeburg statt. Seit dem Jahr 1996 wird der Theorietag von einem eintägigen Workshop mit eingeladenen Vorträgen begleitet. Die Jahrestagung der Fachgruppe Logik in der Informatik der Gesellschaft für Informatik fand erstmals 1993 in Leipzig statt. Im Laufe beider Jahrestagungen finden auch die jährliche Fachgruppensitzungen statt. In diesem Jahr wird der Theorietag der Fachgruppe Automaten und Formale Sprachen erstmalig zusammen mit der Jahrestagung der Fachgruppe Logik in der Informatik abgehalten. Organisiert wurde die gemeinsame Veranstaltung von der Arbeitsgruppe Zuverlässige Systeme des Instituts für Informatik an der Christian-Albrechts-Universität Kiel vom 4. bis 7. Oktober im Tagungshotel Tannenfelde bei Neumünster. Während des Tre↵ens wird ein Workshop für alle Interessierten statt finden. In Tannenfelde werden • Christoph Löding (Aachen) • Tomás Masopust (Dresden) • Henning Schnoor (Kiel) • Nicole Schweikardt (Berlin) • Georg Zetzsche (Paris) eingeladene Vorträge zu ihrer aktuellen Arbeit halten. Darüber hinaus werden 26 Vorträge von Teilnehmern und Teilnehmerinnen gehalten, 17 auf dem Theorietag Automaten und formale Sprachen und neun auf der Jahrestagung Logik in der Informatik. Der vorliegende Band enthält Kurzfassungen aller Beiträge. Wir danken der Gesellschaft für Informatik, der Christian-Albrechts-Universität zu Kiel und dem Tagungshotel Tannenfelde für die Unterstützung dieses Theorietags. Ein besonderer Dank geht an das Organisationsteam: Maike Bradler, Philipp Sieweck, Joel Day. Kiel, Oktober 2016 Florin Manea, Dirk Nowotka und Thomas Wilk
Weakly-Unambiguous Parikh Automata and Their Link to Holonomic Series
We investigate the connection between properties of formal languages and properties of their generating series, with a focus on the class of holonomic power series. We first prove a strong version of a conjecture by Castiglione and Massazza: weakly-unambiguous Parikh automata are equivalent to unambiguous two-way reversal bounded counter machines, and their multivariate generating series are holonomic. We then show that the converse is not true: we construct a language whose generating series is algebraic (thus holonomic), but which is inherently weakly-ambiguous as a Parikh automata language. Finally, we prove an effective decidability result for the inclusion problem for weakly-unambiguous Parikh automata, and provide an upper-bound on its complexity
Ambiguity through the lens of measure theory
In this paper, we consider automata accepting irreducible sofic shifts, that
is, strongly connected automata where each state is initial and final. We
provide a characterization of unambiguity for finite words by means of measure
of sets of infinite sequences labelling two runs. More precisely, we show that
such an automaton is unambiguous, in the sense that no finite word labels two
runs with the same starting state and the same ending state if and only if for
each state, the set of infinite sequences labelling two runs starting from that
state has measure zero
Bidimensional Linear Recursive Sequences and Universality of Unambiguous Register Automata
We study the universality and inclusion problems for register automata over
equality data. We show that the universality and the inclusion problems can be
solved with 2-EXPTIME complexity when the input automata are without guessing
and unambiguous, improving on the currently best-known 2-EXPSPACE upper bound
by Mottet and Quaas. When the number of registers of both automata is fixed, we
obtain a lower EXPTIME complexity, also improving the EXPSPACE upper bound from
Mottet and Quaas for fixed number of registers. We reduce inclusion to
universality, and then we reduce universality to the problem of counting the
number of orbits of runs of the automaton. We show that the orbit-counting
function satisfies a system of bidimensional linear recursive equations with
polynomial coefficients (linrec), which generalises analogous recurrences for
the Stirling numbers of the second kind, and then we show that universality
reduces to the zeroness problem for linrec sequences. While such a counting
approach is classical and has successfully been applied to unambiguous finite
automata and grammars over finite alphabets, its application to register
automata over infinite alphabets is novel. We provide two algorithms to decide
the zeroness problem for bidimensional linear recursive sequences arising from
orbit-counting functions. Both algorithms rely on techniques from linear
non-commutative algebra. The first algorithm performs variable elimination and
has elementary complexity. The second algorithm is a refined version of the
first one and it relies on the computation of the Hermite normal form of
matrices over a skew polynomial field. The second algorithm yields an EXPTIME
decision procedure for the zeroness problem of linrec sequences, which in turn
yields the claimed bounds for the universality and inclusion problems of
register automata.Comment: full version of the homonymous paper to appear in the proceedings of
STACS'2
A Bit of Nondeterminism Makes Pushdown Automata Expressive and Succinct
We study the expressiveness and succinctness of good-for-games pushdown automata (GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. We prove that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal to unambiguous CFL. We further show that GFG-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than GFG-PDA. We also study GFGness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show GFGness to be EXPTIME-complete. GFG-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than GFG-VPA. Both of these lower bounds are tight. Finally, we study the complexity of resolving nondeterminism in GFG-PDA. Every GFG-PDA has a positional resolver, a function that resolves nondeterminism and that is only dependant on the current configuration. Pushdown transducers are sufficient to implement the resolvers of GFG-VPA, but not those of GFG-PDA. GFG-PDA with finite-state resolvers are determinisable