Commutative Data Automata

Formalisms over infinite alphabets have recently received much focus in the community of the-oretical computer science. Data automata is a formal model for words over infinite alphabets proposed by Bojanczyk, Muscholl, Schwentick et. al. in 2006. A data automaton consists of two parts, a nondeterministic letter-to-letter transducer, and a class condition specified by a finite automaton over the output alphabet of the transducer, which acts as a condition on the subsequence of the outputs of the transducer in every class, namely, in every maximal set of po-sitions with the same data value. It is open whether the nonemptiness of data automata can be decided with elementary complexity. Very recently, a restriction of data automata with element-ary complexity, called weak data automata, was proposed by Kara, Schwentick and Tan and its nonemptiness problem was shown to be in 2-NEXPTIME. In weak data automata, the class condi-tions are specified by some simple constraints on the number of occurrences of labels occurring in every class. The aim of this paper is to demonstrate that the commutativity of class conditions is the genuine reason accounting for the elementary complexity of weak data automata. For this purpose, we define and investigate commutative data automata, which are data automata with class conditions restricted to commutative regular languages. We show that while the express-ive power of commutative data automata is strictly stronger than that of weak data automata, the nonemptiness problem of this model can still be decided with elementary complexity, more precisely, in 3-NEXPTIME. In addition, we extend the results to data ω-words and prove that the nonemptiness of commutative Büchi data automata can be decided in 4-NEXPTIME. We also provide logical characterizations for commutative (Büchi) data automata, similar to those for weak (Büchi) data automata

Single-Use Automata and Transducers for Infinite Alphabets

Our starting point are register automata for data words, in the style of Kaminski and Francez. We study the effects of the single-use restriction, which says that a register is emptied immediately after being used. We show that under the single-use restriction, the theory of automata for data words becomes much more robust. The main results are: (a) five different machine models are equivalent as language acceptors, including one-way and two-way single-use register automata; (b) one can recover some of the algebraic theory of languages over finite alphabets, including a version of the Krohn-Rhodes Theorem; (c) there is also a robust theory of transducers, with four equivalent models, including two-way single use transducers and a variant of streaming string transducers for data words. These results are in contrast with automata for data words without the single-use restriction, where essentially all models are pairwise non-equivalent

History-Register Automata

Programs with dynamic allocation are able to create and use an unbounded number of fresh resources, such as references, objects, files, etc. We propose History-Register Automata (HRA), a new automata-theoretic formalism for modelling such programs. HRAs extend the expressiveness of previous approaches and bring us to the limits of decidability for reachability checks. The distinctive feature of our machines is their use of unbounded memory sets (histories) where input symbols can be selectively stored and compared with symbols to follow. In addition, stored symbols can be consumed or deleted by reset. We show that the combination of consumption and reset capabilities renders the automata powerful enough to imitate counter machines, and yields closure under all regular operations apart from complementation. We moreover examine weaker notions of HRAs which strike different balances between expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS

Set Augmented Finite Automata over Infinite Alphabets

A data language is a set of finite words defined on an infinite alphabet. Data languages are used to express properties associated with data values (domain defined over a countably infinite set). In this paper, we introduce set augmented finite automata (SAFA), a new class of automata for expressing data languages. We investigate the decision problems, closure properties, and expressiveness of SAFA. We also study the deterministic variant of these automata.Comment: This is a full version of a paper with the same name accepted in DLT 2023. Other than the full proofs, this paper contains several new results concerning more closure properties, universality problem, comparison of expressiveness with register automata and class counter automata, and more results on deterministic SAF

Algorithmic Analysis of Array-Accessing Programs

For programs whose data variables range over Boolean or finite domains, program verification is decidable, and this forms the basis of recent tools for software model checking. In this paper, we consider algorithmic verification of programs that use Boolean variables, and in addition, access a single array whose length is potentially unbounded, and whose elements range over pairs from Σ × D, where Σ is a finite alphabet and D is a potentially unbounded data domain. We show that the reachability problem, while undecidable in general, is (1) Pspace-complete for programs in which the array-accessing for-loops are not nested, (2) solvable in Ex-pspace for programs with arbitrarily nested loops if array elements range over a finite data domain, and (3) decidable for a restricted class of programs with doubly-nested loops. The third result establishes connections to automata and logics defining languages over data words

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

Querying graphs with data

Graph data is becoming more and more pervasive. Indeed, services such as Social Networks or the Semantic Web can no longer rely on the traditional relational model, as its structure is somewhat too rigid for the applications they have in mind. For this reason we have seen a continuous shift towards more non-standard models. First it was the semi-structured data in the 1990s and XML in 2000s, but even such models seem to be too restrictive for new applications that require navigational properties naturally modelled by graphs. Social networks fit into the graph model by their very design: users are nodes and their connections are specified by graph edges. The W3C committee, on the other hand, describes RDF, the model underlying the Semantic Web, by using graphs. The situation is quite similar with crime detection networks and tracking workflow provenance, namely they all have graphs inbuilt into their definition. With pervasiveness of graph data the important question of querying and maintaining it has emerged as one of the main priorities, both in theoretical and applied sense. Currently there seem to be two approaches to handling such data. On the one hand, to extract the actual data, practitioners use traditional relational languages that completely disregard various navigational patterns connecting the data. What makes this data interesting in modern applications, however, is precisely its ability to compactly represent intricate topological properties that envelop the data. To overcome this issue several languages that allow querying graph topology have been proposed and extensively studied. The problem with these languages is that they concentrate on navigation only, thus disregarding the data that is actually stored in the database. What we propose in this thesis is the ability to do both. Namely, we will study how query languages can be designed to allow specifying not only how the data is connected, but also how data changes along paths and patterns connecting it. To this end we will develop several query languages and show how adding different data manipulation capabilities and different navigational features affects the complexity of main reasoning tasks. The story here is somewhat similar to the early success of the relational data model, where theoretical considerations led to a better understanding of what makes certain tasks more challenging than others. Here we aim for languages that are both efficient and capable of expressing a wide variety of queries of interest to several groups of practitioners. To do so we will analyse how different requirements affect the language at hand and at the end provide a good base of primitives whose inclusion into a language should be considered, based on the applications one has in mind. Namely, we consider how adding a specific operation, mechanism, or capability to the language affects practical tasks that such an addition plans to tackle. In the end we arrive at several languages, all of them with their pros and cons, giving us a good overview of how specific capabilities of the language affect the design goals, thus providing a sound basis for practitioners to choose from, based on their requirements

Fault tolerance issues in nanoelectronics

The astonishing success story of microelectronics cannot go on indefinitely. In fact, once devices reach the few-atom scale (nanoelectronics), transient quantum effects are expected to impair their behaviour. Fault tolerant techniques will then be required. The aim of this thesis is to investigate the problem of transient errors in nanoelectronic devices. Transient error rates for a selection of nanoelectronic gates, based upon quantum cellular automata and single electron devices, in which the electrostatic interaction between electrons is used to create Boolean circuits, are estimated. On the bases of such results, various fault tolerant solutions are proposed, for both logic and memory nanochips. As for logic chips, traditional techniques are found to be unsuitable. A new technique, in which the voting approach of triple modular redundancy (TMR) is extended by cascading TMR units composed of nanogate clusters, is proposed and generalised to other voting approaches. For memory chips, an error correcting code approach is found to be suitable. Various codes are considered and a lookup table approach is proposed for encoding and decoding. We are then able to give estimations for the redundancy level to be provided on nanochips, so as to make their mean time between failures acceptable. It is found that, for logic chips, space redundancies up to a few tens are required, if mean times between failures have to be of the order of a few years. Space redundancy can also be traded for time redundancy. As for memory chips, mean times between failures of the order of a few years are found to imply both space and time redundancies of the order of ten

Metric propositional neighborhood logic with an equivalence relation

The propositional interval logic of temporal neighborhood (PNL for short) features two modalities that make it possible to access intervals adjacent to the right (modality \u27e8 A\u27e9) and to the left (modality \u27e8 A\uaf \u27e9) of the current interval. PNL stands at a central position in the realm of interval temporal logics, as it is expressive enough to encode meaningful temporal conditions and decidable (undecidability rules over interval temporal logics, while PNL is NEXPTIME-complete). Moreover, it is expressively complete with respect to the two-variable fragment of first-order logic extended with a linear order FO 2[<]. Various extensions of PNL have been studied in the literature, including metric, hybrid, and first-order ones. Here, we study the effects of the addition of an equivalence relation 3c to Metric PNL (MPNL 3c). We first show that the finite satisfiability problem for PNL extended with 3c is still NEXPTIME-complete. Then, we prove that the same problem for MPNL 3c can be reduced to the decidable 0\u20130 reachability problem for vector addition systems and vice versa (EXPSPACE-hardness immediately follows)