Revisiting Underapproximate Reachability for Multipushdown Systems

Boolean programs with multiple recursive threads can be captured as pushdown automata with multiple stacks. This model is Turing complete, and hence, one is often interested in analyzing a restricted class that still captures useful behaviors. In this paper, we propose a new class of bounded under approximations for multi-pushdown systems, which subsumes most existing classes. We develop an efficient algorithm for solving the under-approximate reachability problem, which is based on efficient fix-point computations. We implement it in our tool BHIM and illustrate its applicability by generating a set of relevant benchmarks and examining its performance. As an additional takeaway, BHIM solves the binary reachability problem in pushdown automata. To show the versatility of our approach, we then extend our algorithm to the timed setting and provide the first implementation that can handle timed multi-pushdown automata with closed guards.Comment: 52 pages, Conference TACAS 202

Optimised determinisation and completion of finite tree automata

Determinisation and completion of finite tree automata are important operations with applications in program analysis and verification. However, the complexity of the classical procedures for determinisation and completion is high. They are not practical procedures for manipulating tree automata beyond very small ones. In this paper we develop an algorithm for determinisation and completion of finite tree automata, whose worst-case complexity remains unchanged, but which performs far better than existing algorithms in practice. The critical aspect of the algorithm is that the transitions of the determinised (and possibly completed) automaton are generated in a potentially very compact form called product form, which can reduce the size of the representation dramatically. Furthermore, the representation can often be used directly when manipulating the determinised automaton. The paper contains an experimental evaluation of the algorithm on a large set of tree automata examples

Stream Processing using Grammars and Regular Expressions

In this dissertation we study regular expression based parsing and the use of grammatical specifications for the synthesis of fast, streaming string-processing programs. In the first part we develop two linear-time algorithms for regular expression based parsing with Perl-style greedy disambiguation. The first algorithm operates in two passes in a semi-streaming fashion, using a constant amount of working memory and an auxiliary tape storage which is written in the first pass and consumed by the second. The second algorithm is a single-pass and optimally streaming algorithm which outputs as much of the parse tree as is semantically possible based on the input prefix read so far, and resorts to buffering as many symbols as is required to resolve the next choice. Optimality is obtained by performing a PSPACE-complete pre-analysis on the regular expression. In the second part we present Kleenex, a language for expressing high-performance streaming string processing programs as regular grammars with embedded semantic actions, and its compilation to streaming string transducers with worst-case linear-time performance. Its underlying theory is based on transducer decomposition into oracle and action machines, and a finite-state specialization of the streaming parsing algorithm presented in the first part. In the second part we also develop a new linear-time streaming parsing algorithm for parsing expression grammars (PEG) which generalizes the regular grammars of Kleenex. The algorithm is based on a bottom-up tabulation algorithm reformulated using least fixed points and evaluated using an instance of the chaotic iteration scheme by Cousot and Cousot

On space efficiency of algorithms working on structural decompositions of graphs

Dynamic programming on path and tree decompositions of graphs is a technique that is ubiquitous in the field of parameterized and exponential-time algorithms. However, one of its drawbacks is that the space usage is exponential in the decomposition's width. Following the work of Allender et al. [Theory of Computing, '14], we investigate whether this space complexity explosion is unavoidable. Using the idea of reparameterization of Cai and Juedes [J. Comput. Syst. Sci., '03], we prove that the question is closely related to a conjecture that the Longest Common Subsequence problem parameterized by the number of input strings does not admit an algorithm that simultaneously uses XP time and FPT space. Moreover, we complete the complexity landscape sketched for pathwidth and treewidth by Allender et al. by considering the parameter tree-depth. We prove that computations on tree-depth decompositions correspond to a model of non-deterministic machines that work in polynomial time and logarithmic space, with access to an auxiliary stack of maximum height equal to the decomposition's depth. Together with the results of Allender et al., this describes a hierarchy of complexity classes for polynomial-time non-deterministic machines with different restrictions on the access to working space, which mirrors the classic relations between treewidth, pathwidth, and tree-depth.Comment: An extended abstract appeared in the proceedings of STACS'16. The new version is augmented with a space-efficient algorithm for Dominating Set using the Chinese remainder theore

Subtyping and application of context-free classes

Object-oriented systems are usually not designed from scratch but constructed using frameworks or class libraries. This construction should lead to correct systems provided the reused classes are locally correct. Therefore knowledge about the features that a certain class provides is often not enough. It is additionally necessary to know the correct semantics of classes, i.e. information on how to use these features. Especially, we have to mind the sequences of method calls that are acceptable by an object. Using regular languages for the description of these sequences works fine for some classes but is not adequate for others, e.g. for stacks, buffers, queues or lists etc. In this paper we present a more general approach for the specification of the dynamic behavior of objects using context-free grammars. We investigate questions of correctness in subtyping and application of such classes. We define sufficient conditions for class systems such that local correctness in subtyping and application implies global correctness of the system

Origin-equivalence of two-way word transducers is in PSPACE

We consider equivalence and containment problems for word transductions. These problems are known to be undecidable when the transductions are relations between words realized by non-deterministic transducers, and become decidable when restricting to functions from words to words. Here we prove that decidability can be equally recovered the origin semantics, that was introduced by Bojanczyk in 2014. We prove that the equivalence and containment problems for two-way word transducers in the origin semantics are PSPACE-complete. We also consider a variant of the containment problem where two-way transducers are compared under the origin semantics, but in a more relaxed way, by allowing distortions of the origins. The possible distortions are described by means of a resynchronization relation. We propose MSO-definable resynchronizers and show that they preserve the decidability of the containment problem under resynchronizations. {

Automata and linear temporal logic : translations with transition-based acceptance

Automata theory provides powerful tools for designing and implementing decision procedures for temporal logics and their applications to the automatic verification of systems against their logical specifications. Implementing these decision procedures by making use of automata built from the systems and their specifications with translation procedures is challenging in practice due to the tendency of the automata to grow easily unmanageably large as the size of the systems or the logical specifications increases. This thesis develops the theory of translating propositional linear time temporal logic (LTL) into nondeterministic automata via self-loop alternating automata. Unlike nondeterministic automata, self-loop alternating automata are expressively equivalent to LTL and allow a conceptually simple translation of LTL specifications into automata using a set of rules for building automata incrementally from smaller components. The use of generalized transition-based acceptance for automata throughout all constructions gives rise to new optimized translation rules and facilitates designing heuristics for the minimization of automata by making use of language containment tests combined with structural analysis of automata. The generalized definition also supports the translation of self-loop alternating automata into nondeterministic automata by essentially applying the standard subset construction; this construction can be further simplified and optimized when working with automata built from LTL formulas. The translation rules can also be used to identify a syntactic subclass of LTL for which the exponential increase caused by the subset construction in the number of states of the automaton can always be avoided; consequently, the satisfiability problem for this subclass, which is shown to extend related subclasses known from the literature, is NP-complete. Additionally, the emptiness of generalized nondeterministic automata is shown to be testable without giving up generalized transition-based acceptance by using a new variant of the well-known nested depth-first search algorithm with improved worst-case resource requirements.Automaattiteorian avulla voidaan suunnitella ja toteuttaa temporaalilogiikkojen ratkaisumenetelmiä sekä näiden menetelmien sovellutuksia logiikoilla järjestelmistä esitettyjen oikeellisuusvaatimusten tietokoneavusteiseen verifiointiin. Käytännössä näiden ratkaisumenetelmien toteuttaminen kääntämällä järjestelmät ja niiden oikeellisuusvaatimukset automaateiksi on kuitenkin haasteellista, sillä näistä automaateista tulee järjestelmien tai loogisten vaatimusten koon kasvaessa helposti niin suuria, ettei niitä enää voida käsitellä. Tässä väitöskirjassa kehitetään lineaarisen ajan temporaalilogiikan (LTL) epädeterministisiksi automaateiksi kääntämisen teoriaa käyttämällä käännöksen apuna vain yhden tilan silmukoita sisältäviä alternoivia automaatteja, joilla – toisin kuin epädeterministisillä automaateilla – on sama ilmaisuvoima kuin lineaarisen ajan temporaalilogiikalla. Tätä logiikkaa voidaan kääntää näiksi automaateiksi soveltaen yksinkertaisia sääntöjä automaattien yhdistämiseksi vaiheittain keskenään yhä suuremmiksi automaateiksi. Käyttämällä yleistettyä siirtymäpohjaista hyväksyvyyden määritelmää automaateille kaikissa käännöksen vaiheissa voidaan näin muodostettuja automaatteja sieventää uusin tavoin käyttäen apuna automaattien hyväksymien kielten välisiä sisältyvyyssuhteita sekä automaattien rakenteellisia ominaisuuksia. Yleistetyn määritelmän ansiosta vain yhden tilan silmukoita sisältävät alternoivat automaatit voidaan myös kääntää edelleen epädeterministisiksi automaateiksi soveltamalla yleisesti tunnettua osajoukkokonstruktiota lähes sellaisenaan. Tämä konstruktio voidaan edelleen tehdä yksinkertaisemmin ja tehokkaammin LTL-kaavoista muodostetuille automaateille. Automaattikäännöksessä käytettävien sääntöjen avulla voidaan myös erottaa lineaarisen ajan temporaalilogiikan syntaktinen osajoukko, jonka kaavat onmahdollista kääntää epädeterministisiksi automaateiksi ilman, että automaattien tilojen määrä kasvaa osajoukkokonstruktion tavoin eksponentiaalisesti. Tästä tuloksesta seuraa, että kyseisen LTL:n osajoukon toteutuvuusongelma on NP-täydellinen. Osajoukko on samankaltaisia kirjallisuudessa aiemmin esiteltyjä osajoukkoja aidosti laajempi. Väitöskirjassa esitetään myös, kuinka epädeterministisen automaatin hyväksymän kielen tyhjyys voidaan tarkastaa luopumatta yleistetystä siirtymäpohjaisesta hyväksyvyyden määritelmästä käyttäen algoritmia, joka on uusi, huonoimman tapauksen vaatimuksiltaan tehokkaampi muunnos tunnetusta sisäkkäisestä syvyyshakualgoritmista.reviewe

Logic and Automata

Mathematical logic and automata theory are two scientific disciplines with a fundamentally close relationship. The authors of Logic and Automata take the occasion of the sixtieth birthday of Wolfgang Thomas to present a tour d'horizon of automata theory and logic. The twenty papers in this volume cover many different facets of logic and automata theory, emphasizing the connections to other disciplines such as games, algorithms, and semigroup theory, as well as discussing current challenges in the field