Logics for Unranked Trees: An Overview

Labeled unranked trees are used as a model of XML documents, and logical languages for them have been studied actively over the past several years. Such logics have different purposes: some are better suited for extracting data, some for expressing navigational properties, and some make it easy to relate complex properties of trees to the existence of tree automata for those properties. Furthermore, logics differ significantly in their model-checking properties, their automata models, and their behavior on ordered and unordered trees. In this paper we present a survey of logics for unranked trees

Global Numerical Constraints on Trees

We introduce a logical foundation to reason on tree structures with constraints on the number of node occurrences. Related formalisms are limited to express occurrence constraints on particular tree regions, as for instance the children of a given node. By contrast, the logic introduced in the present work can concisely express numerical bounds on any region, descendants or ancestors for instance. We prove that the logic is decidable in single exponential time even if the numerical constraints are in binary form. We also illustrate the usage of the logic in the description of numerical constraints on multi-directional path queries on XML documents. Furthermore, numerical restrictions on regular languages (XML schemas) can also be concisely described by the logic. This implies a characterization of decidable counting extensions of XPath queries and XML schemas. Moreover, as the logic is closed under negation, it can thus be used as an optimal reasoning framework for testing emptiness, containment and equivalence

Efficient CTL Verification via Horn Constraints Solving

The use of temporal logics has long been recognised as a fundamental approach to the formal specification and verification of reactive systems. In this paper, we take on the problem of automatically verifying a temporal property, given by a CTL formula, for a given (possibly infinite-state) program. We propose a method based on encoding the problem as a set of Horn constraints. The method takes a program, modeled as a transition system, and a property given by a CTL formula as input. It first generates a set of forall-exists quantified Horn constraints and well-foundedness constraints by exploiting the syntactic structure of the CTL formula. Then, the generated set of constraints are solved by applying an off-the-shelf Horn constraints solving engine. The program is said to satisfy the property if and only if the generated set of constraints has a solution. We demonstrate the practical promises of the method by applying it on a set of challenging examples. Although our method is based on a generic Horn constraint solving engine, it is able to outperform state-of-art methods specialised for CTL verification.Comment: In Proceedings HCVS2016, arXiv:1607.0403

Generalization Strategies for the Verification of Infinite State Systems

We present a method for the automated verification of temporal properties of infinite state systems. Our verification method is based on the specialization of constraint logic programs (CLP) and works in two phases: (1) in the first phase, a CLP specification of an infinite state system is specialized with respect to the initial state of the system and the temporal property to be verified, and (2) in the second phase, the specialized program is evaluated by using a bottom-up strategy. The effectiveness of the method strongly depends on the generalization strategy which is applied during the program specialization phase. We consider several generalization strategies obtained by combining techniques already known in the field of program analysis and program transformation, and we also introduce some new strategies. Then, through many verification experiments, we evaluate the effectiveness of the generalization strategies we have considered. Finally, we compare the implementation of our specialization-based verification method to other constraint-based model checking tools. The experimental results show that our method is competitive with the methods used by those other tools. To appear in Theory and Practice of Logic Programming (TPLP).Comment: 24 pages, 2 figures, 5 table

Proceedings of the Joint Automated Reasoning Workshop and Deduktionstreffen: As part of the Vienna Summer of Logic – IJCAR 23-24 July 2014

Preface For many years the British and the German automated reasoning communities have successfully run independent series of workshops for anybody working in the area of automated reasoning. Although open to the general public they addressed in the past primarily the British and the German communities, respectively. At the occasion of the Vienna Summer of Logic the two series have a joint event in Vienna as an IJCAR workshop. In the spirit of the two series there will be only informal proceedings with abstracts of the works presented. These are collected in this document. We have tried to maintain the informal open atmosphere of the two series and have welcomed in particular research students to present their work. We have solicited for all work related to automated reasoning and its applications with a particular interest in work-in-progress and the presentation of half-baked ideas. As in the previous years, we have aimed to bring together researchers from all areas of automated reasoning in order to foster links among researchers from various disciplines; among theoreticians, implementers and users alike, and among international communities, this year not just the British and German communities

Revisiting Parameter Synthesis for One-Counter Automata

We study the synthesis problem for one-counter automata with parameters. One-counter automata are obtained by extending classical finite-state automata with a counter whose value can range over non-negative integers and be tested for zero. The updates and tests applicable to the counter can further be made parametric by introducing a set of integer-valued variables called parameters. The synthesis problem for such automata asks whether there exists a valuation of the parameters such that all infinite runs of the automaton satisfy some ?-regular property. Lechner showed that (the complement of) the problem can be encoded in a restricted one-alternation fragment of Presburger arithmetic with divisibility. In this work (i) we argue that said fragment, called ??_RPAD^+, is unfortunately undecidable. Nevertheless, by a careful re-encoding of the problem into a decidable restriction of ??_RPAD^+, (ii) we prove that the synthesis problem is decidable in general and in 2NEXP for several fixed ?-regular properties. Finally, (iii) we give polynomial-space algorithms for the special cases of the problem where parameters can only be used in counter tests