The Degree of Word-Expansion of Lexicalized RRWW-Automata

F. Mráz and M.Plátek were supported by the program 'Information Society' under project 1ET100300517. F. Mráz was also supported by the Grant Agency of Charles University in Prague under Grant-No. 358/2006/A-INF/MFF.Einige der Ergebnisse dieser Arbeit wurden auf der CIAA 2007 in Prag (Juli 2007) vorgestellt. Der entsprechende Beitrag mit dem Titel "A measure for the degree of nondeterminism of context-free languages" steht auf den Seiten 192-202 im Tagungsband dieser Konferenz. Titel des Tagungsbandes: "Implementation and Application of Automata", 12th International Conference, CIAA 2007, Prague, Czech Republic, July 16-18, 2007, Revised Selected Papers. Serie: "Lecture Notes in Computer Science". Erschienen am 24.10.07 im Springer Verlag Berlin. ISBN 978-3-54-76335-

Methods for Structural Pattern Recognition: Complexity and Applications

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Proceedings

Proceedings of the NODALIDA 2011 Workshop Constraint Grammar Applications. Editors: Eckhard Bick, Kristin Hagen, Kaili Müürisep, Trond Trosterud. NEALT Proceedings Series, Vol. 14 (2011), vi+69 pp. © 2011 The editors and contributors. Published by Northern European Association for Language Technology (NEALT) http://omilia.uio.no/nealt . Electronically published at Tartu University Library (Estonia) http://hdl.handle.net/10062/19231

Order-Related Problems Parameterized by Width

In the main body of this thesis, we study two different order theoretic problems. The first problem, called Completion of an Ordering, asks to extend a given finite partial order to a complete linear order while respecting some weight constraints. The second problem is an order reconfiguration problem under width constraints. While the Completion of an Ordering problem is NP-complete, we show that it lies in FPT when parameterized by the interval width of ρ. This ordering problem can be used to model several ordering problems stemming from diverse application areas, such as graph drawing, computational social choice, and computer memory management. Each application yields a special partial order ρ. We also relate the interval width of ρ to parameterizations for these problems that have been studied earlier in the context of these applications, sometimes improving on parameterized algorithms that have been developed for these parameterizations before. This approach also gives some practical sub-exponential time algorithms for ordering problems. In our second main result, we combine our parameterized approach with the paradigm of solution diversity. The idea of solution diversity is that instead of aiming at the development of algorithms that output a single optimal solution, the goal is to investigate algorithms that output a small set of sufficiently good solutions that are sufficiently diverse from one another. In this way, the user has the opportunity to choose the solution that is most appropriate to the context at hand. It also displays the richness of the solution space. There, we show that the considered diversity version of the Completion of an Ordering problem is fixed-parameter tractable with respect to natural paramaters that capture the notion of diversity and the notion of sufficiently good solutions. We apply this algorithm in the study of the Kemeny Rank Aggregation class of problems, a well-studied class of problems lying in the intersection of order theory and social choice theory. Up to this point, we have been looking at problems where the goal is to find an optimal solution or a diverse set of good solutions. In the last part, we shift our focus from finding solutions to studying the solution space of a problem. There we consider the following order reconfiguration problem: Given a graph G together with linear orders τ and τ ′ of the vertices of G, can one transform τ into τ ′ by a sequence of swaps of adjacent elements in such a way that at each time step the resulting linear order has cutwidth (pathwidth) at most w? We show that this problem always has an affirmative answer when the input linear orders τ and τ ′ have cutwidth (pathwidth) at most w/2. Using this result, we establish a connection between two apparently unrelated problems: the reachability problem for two-letter string rewriting systems and the graph isomorphism problem for graphs of bounded cutwidth. This opens an avenue for the study of the famous graph isomorphism problem using techniques from term rewriting theory. In addition to the main part of this work, we present results on two unrelated problems, namely on the Steiner Tree problem and on the Intersection Non-emptiness problem from automata theory.Doktorgradsavhandlin

Taming Strings in Dynamic Languages - An Abstract Interpretation-based Static Analysis Approach

In the recent years, dynamic languages such as JavaScript, Python or PHP, have found several fields of applications, thanks to the multiple features provided, the agility of deploying software and the seeming facility of learning such languages. In particular, strings play a central role in dynamic languages, as they can be implicitly converted to other type values, used to access object properties or transformed at run-time into executable code. In particular, the possibility to dynamically generate code as strings transformation breaks the typical assumption in static program analysis that the code is an immutable object, indeed static. This happens because program\u2019s essential data structures, such as the control-flow graph and the system of equation associated with the program to analyze, are themselves dynamically mutating objects. In a sentence: "You can\u2019t check the code you don\u2019t see". For all these reasons, dynamic languages still pone a big challenge for static program analysis, making it drastically hard and imprecise. The goal of this thesis is to tackle the problem of statically analyzing dynamic code by treating the code as any other data structure that can be statically analyzed, and by treating the static analyzer as any other function that can be recursively called. Since, in dynamically-generated code, the program code can be encoded as strings and then transformed into executable code, we first define a novel and suitable string abstraction, and the corresponding abstract semantics, able to both keep enough information to analyze string properties, in general, and keep enough information about the possible executable strings that may be converted to code. Such string abstraction will permits us to distill from a string abstract value the executable program expressed by it, allowing us to recursively call the static analyzer on the synthesized program. The final result of this thesis is an important first step towards a sound-by- construction abstract interpreter for real-world dynamic string manipulation languages, analyzing also string-to-code statements, that is the code that standard static analysis "can\u2019t see"

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems