542 research outputs found
In the Maze of Data Languages
In data languages the positions of strings and trees carry a label from a
finite alphabet and a data value from an infinite alphabet. Extensions of
automata and logics over finite alphabets have been defined to recognize data
languages, both in the string and tree cases. In this paper we describe and
compare the complexity and expressiveness of such models to understand which
ones are better candidates as regular models
Synchronizing Deterministic Push-Down Automata Can Be Really Hard
The question if a deterministic finite automaton admits a software reset in the form of a so-called synchronizing word can be answered in polynomial time. In this paper, we extend this algorithmic question to deterministic automata beyond finite automata. We prove that the question of synchronizability becomes undecidable even when looking at deterministic one-counter automata. This is also true for another classical mild extension of regularity, namely that of deterministic one-turn push-down automata. However, when we combine both restrictions, we arrive at scenarios with a PSPACE-complete (and hence decidable) synchronizability problem. Likewise, we arrive at a decidable synchronizability problem for (partially) blind deterministic counter automata.
There are several interpretations of what synchronizability should mean for deterministic push-down automata. This is depending on the role of the stack: should it be empty on synchronization, should it be always the same or is it arbitrary? For the automata classes studied in this paper, the complexity or decidability status of the synchronizability problem is mostly independent of this technicality, but we also discuss one class of automata where this makes a difference
Decision Problems for Subclasses of Rational Relations over Finite and Infinite Words
We consider decision problems for relations over finite and infinite words
defined by finite automata. We prove that the equivalence problem for binary
deterministic rational relations over infinite words is undecidable in contrast
to the case of finite words, where the problem is decidable. Furthermore, we
show that it is decidable in doubly exponential time for an automatic relation
over infinite words whether it is a recognizable relation. We also revisit this
problem in the context of finite words and improve the complexity of the
decision procedure to single exponential time. The procedure is based on a
polynomial time regularity test for deterministic visibly pushdown automata,
which is a result of independent interest.Comment: v1: 31 pages, submitted to DMTCS, extended version of the paper with
the same title published in the conference proceedings of FCT 2017; v2: 32
pages, minor revision of v1 (DMTCS review process), results unchanged; v3: 32
pages, enabled hyperref for Figure 1; v4: 32 pages, add reference for known
complexity results for the slenderness problem; v5: 32 pages, added DMTCS
metadat
Programming Using Automata and Transducers
Automata, the simplest model of computation, have proven to be an effective tool in reasoning about programs that operate over strings. Transducers augment automata to produce outputs and have been used to model string and tree transformations such as natural language translations. The success of these models is primarily due to their closure properties and decidable procedures, but good properties come at the price of limited expressiveness. Concretely, most models only support finite alphabets and can only represent small classes of languages and transformations. We focus on addressing these limitations and bridge the gap between the theory of automata and transducers and complex real-world applications: Can we extend automata and transducer models to operate over structured and infinite alphabets? Can we design languages that hide the complexity of these formalisms? Can we define executable models that can process the input efficiently? First, we introduce succinct models of transducers that can operate over large alphabets and design BEX, a language for analysing string coders. We use BEX to prove the correctness of UTF and BASE64 encoders and decoders. Next, we develop a theory of tree transducers over infinite alphabets and design FAST, a language for analysing tree-manipulating programs. We use FAST to detect vulnerabilities in HTML sanitizers, check whether augmented reality taggers conflict, and optimize and analyze functional programs that operate over lists and trees. Finally, we focus on laying the foundations of stream processing of hierarchical data such as XML files and program traces. We introduce two new efficient and executable models that can process the input in a left-to-right linear pass: symbolic visibly pushdown automata and streaming tree transducers. Symbolic visibly pushdown automata are closed under Boolean operations and can specify and efficiently monitor complex properties for hierarchical structures over infinite alphabets. Streaming tree transducers can express and efficiently process complex XML transformations while enjoying decidable procedures
Revisiting Membership Problems in Subclasses of Rational Relations
We revisit the membership problem for subclasses of rational relations over
finite and infinite words: Given a relation R in a class C_2, does R belong to
a smaller class C_1? The subclasses of rational relations that we consider are
formed by the deterministic rational relations, synchronous (also called
automatic or regular) relations, and recognizable relations. For almost all
versions of the membership problem, determining the precise complexity or even
decidability has remained an open problem for almost two decades. In this
paper, we provide improved complexity and new decidability results. (i) Testing
whether a synchronous relation over infinite words is recognizable is
NL-complete (PSPACE-complete) if the relation is given by a deterministic
(nondeterministic) omega-automaton. This fully settles the complexity of this
recognizability problem, matching the complexity of the same problem over
finite words. (ii) Testing whether a deterministic rational binary relation is
recognizable is decidable in polynomial time, which improves a previously known
double exponential time upper bound. For relations of higher arity, we present
a randomized exponential time algorithm. (iii) We provide the first algorithm
to decide whether a deterministic rational relation is synchronous. For binary
relations the algorithm even runs in polynomial time
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
Discounted-Sum Automata with Multiple Discount Factors
Discounting the influence of future events is a key paradigm in economics and
it is widely used in computer-science models, such as games, Markov decision
processes (MDPs), reinforcement learning, and automata. While a single game or
MDP may allow for several different discount factors, discounted-sum automata
(NDAs) were only studied with respect to a single discount factor. For every
integer , as opposed to every , the class of NDAs with discount factor
(-NDAs) has good computational properties: it is closed
under determinization and under the algebraic operations min, max, addition,
and subtraction, and there are algorithms for its basic decision problems, such
as automata equivalence and containment.
We define and analyze discounted-sum automata in which each transition can
have a different integral discount factor (integral NMDAs). We show that
integral NMDAs with an arbitrary choice of discount factors are not closed
under determinization and under algebraic operations and that their containment
problem is undecidable. We then define and analyze a restricted class of
integral NMDAs, which we call tidy NMDAs, in which the choice of discount
factors depends on the prefix of the word read so far. Some of their special
cases are NMDAs that correlate discount factors to actions (alphabet letters)
or to the elapsed time. We show that for every function that defines
the choice of discount factors, the class of -NMDAs enjoys all of the
above good properties of integral NDAs, as well as the same complexity of the
required decision problems. Tidy NMDAs are also as expressive as deterministic
integral NMDAs with an arbitrary choice of discount factors.
All of our results hold for both automata on finite words and automata on
infinite words.Comment: arXiv admin note: text overlap with arXiv:2301.0408
- …