On the Expressive Power of 2-Stack Visibly Pushdown Automata

Visibly pushdown automata are input-driven pushdown automata that recognize some non-regular context-free languages while preserving the nice closure and decidability properties of finite automata. Visibly pushdown automata with multiple stacks have been considered recently by La Torre, Madhusudan, and Parlato, who exploit the concept of visibility further to obtain a rich automata class that can even express properties beyond the class of context-free languages. At the same time, their automata are closed under boolean operations, have a decidable emptiness and inclusion problem, and enjoy a logical characterization in terms of a monadic second-order logic over words with an additional nesting structure. These results require a restricted version of visibly pushdown automata with multiple stacks whose behavior can be split up into a fixed number of phases. In this paper, we consider 2-stack visibly pushdown automata (i.e., visibly pushdown automata with two stacks) in their unrestricted form. We show that they are expressively equivalent to the existential fragment of monadic second-order logic. Furthermore, it turns out that monadic second-order quantifier alternation forms an infinite hierarchy wrt words with multiple nestings. Combining these results, we conclude that 2-stack visibly pushdown automata are not closed under complementation. Finally, we discuss the expressive power of B\"{u}chi 2-stack visibly pushdown automata running on infinite (nested) words. Extending the logic by an infinity quantifier, we can likewise establish equivalence to existential monadic second-order logic

Synthesis through Unification

Given a specification and a set of candidate programs (program space), the program synthesis problem is to find a candidate program that satisfies the specification. We present the synthesis through unification (STUN) approach, which is an extension of the counter-example guided inductive synthesis (CEGIS) approach. In CEGIS, the synthesizer maintains a subset S of inputs and a candidate program Prog that is correct for S. The synthesizer repeatedly checks if there exists a counter-example input c such that the execution of Prog is incorrect on c. If so, the synthesizer enlarges S to include c, and picks a program from the program space that is correct for the new set S. The STUN approach extends CEGIS with the idea that given a program Prog that is correct for a subset of inputs, the synthesizer can try to find a program Prog' that is correct for the rest of the inputs. If Prog and Prog' can be unified into a program in the program space, then a solution has been found. We present a generic synthesis procedure based on the STUN approach and specialize it for three different domains by providing the appropriate unification operators. We implemented these specializations in prototype tools, and we show that our tools often per- forms significantly better on standard benchmarks than a tool based on a pure CEGIS approach

A framework for pathologies of message sequence charts

This is the post-print version of the final paper published in Information Software and Technology. The published article is available from the link below. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. Copyright @ 2012 Elsevier B.V.Context - It is known that a Message Sequence Chart (MSC) specification can contain different types of pathology. However, definitions of different types of pathology and the problems caused by pathologies are unclear, let alone the relationships between them. In this circumstance, it can be problematic for software engineers to accurately predict the possible problems that may exist in implementations of MSC specifications and to trace back to the design problems in MSC specifications from the observed problems of an implementation. Objective - We focus on generating a clearer view on MSC pathologies and building formal relationships between pathologies and the problems that they may cause. Method - By concentrating on the problems caused by pathologies, a categorisation of problems that a distributed system may suffer is first introduced. We investigate the different types of problems and map them to categories of pathologies. Thus, existing concepts related to pathology are refined and necessary concepts in the pathology framework are identified. Finally, we formally prove the relationships between the concepts in the framework. Results - A pathology framework is established as desired based on a restriction that considers problematic scenarios with a single undesirable event. In this framework, we define disjoint categories of both pathologies and the problems caused; the identified types of pathology are successfully mapped to the problems that they may cause. Conclusion - The framework achieved in this paper introduces taxonomies into and clarifies relationships between concepts in research on MSC pathologies. The taxonomies and relationships in the framework can help software engineers to predict problems and verify MSC specifications. The single undesirable event restriction not only enables a categorisation of pathological scenarios, but also has the potential practical benefit that a software engineer can concentrate on key problematic scenarios. This may make it easier to either remove pathologies from an MSC specification MM or test an implementation developed from MM for potential problems resulting from such pathologies

Regular Combinators for String Transformations

We focus on (partial) functions that map input strings to a monoid such as the set of integers with addition and the set of output strings with concatenation. The notion of regularity for such functions has been defined using two-way finite-state transducers, (one-way) cost register automata, and MSO-definable graph transformations. In this paper, we give an algebraic and machine-independent characterization of this class analogous to the definition of regular languages by regular expressions. When the monoid is commutative, we prove that every regular function can be constructed from constant functions using the combinators of choice, split sum, and iterated sum, that are analogs of union, concatenation, and Kleene-*, respectively, but enforce unique (or unambiguous) parsing. Our main result is for the general case of non-commutative monoids, which is of particular interest for capturing regular string-to-string transformations for document processing. We prove that the following additional combinators suffice for constructing all regular functions: (1) the left-additive versions of split sum and iterated sum, which allow transformations such as string reversal; (2) sum of functions, which allows transformations such as copying of strings; and (3) function composition, or alternatively, a new concept of chained sum, which allows output values from adjacent blocks to mix.Comment: This is the full version, with omitted proofs and constructions, of the conference paper currently in submissio

Weak Singular Hybrid Automata

The framework of Hybrid automata, introduced by Alur, Courcourbetis, Henzinger, and Ho, provides a formal modeling and analysis environment to analyze the interaction between the discrete and the continuous parts of cyber-physical systems. Hybrid automata can be considered as generalizations of finite state automata augmented with a finite set of real-valued variables whose dynamics in each state is governed by a system of ordinary differential equations. Moreover, the discrete transitions of hybrid automata are guarded by constraints over the values of these real-valued variables, and enable discontinuous jumps in the evolution of these variables. Singular hybrid automata are a subclass of hybrid automata where dynamics is specified by state-dependent constant vectors. Henzinger, Kopke, Puri, and Varaiya showed that for even very restricted subclasses of singular hybrid automata, the fundamental verification questions, like reachability and schedulability, are undecidable. In this paper we present \emph{weak singular hybrid automata} (WSHA), a previously unexplored subclass of singular hybrid automata, and show the decidability (and the exact complexity) of various verification questions for this class including reachability (NP-Complete) and LTL model-checking (PSPACE-Complete). We further show that extending WSHA with a single unrestricted clock or extending WSHA with unrestricted variable updates lead to undecidability of reachability problem

When images work faster than words: The integration of content-based image retrieval with the Northumbria Watermark Archive

Information on the manufacture, history, provenance, identification, care and conservation of paper-based artwork/objects is disparate and not always readily available. The Northumbria Watermark Archive will incorporate such material into a database, which will be made freely available on the Internet providing an invaluable resource for conservation, research and education. The efficiency of a database is highly dependant on its search mechanism. Text based mechanisms are frequently ineffective when a range of descriptive terminologies might be used i.e. when describing images or translating from foreign languages. In such cases a Content Based Image Retrieval (CBIR) system can be more effective. Watermarks provide paper with unique visual identification characteristics and have been used to provide a point of entry to the archive that is more efficient and effective than a text based search mechanism. The research carried out has the potential to be applied to any numerically large collection of images with distinctive features of colour, shape or texture i.e. coins, architectural features, picture frame profiles, hallmarks, Japanese artists stamps etc. Although the establishment of an electronic archive incorporating a CBIR system can undoubtedly improve access to large collections of images and related data, the development is rarely trouble free. This paper discusses some of the issues that must be considered i.e. collaboration between disciplines; project management; copying and digitising objects; content based image retrieval; the Northumbria Watermark Archive; the use of standardised terminology within a database as well as copyright issues

SyGuS-Comp 2016: Results and Analysis

Syntax-Guided Synthesis (SyGuS) is the computational problem of finding an implementation f that meets both a semantic constraint given by a logical formula $\varphi$ in a background theory T, and a syntactic constraint given by a grammar G, which specifies the allowed set of candidate implementations. Such a synthesis problem can be formally defined in SyGuS-IF, a language that is built on top of SMT-LIB. The Syntax-Guided Synthesis Competition (SyGuS-Comp) is an effort to facilitate, bring together and accelerate research and development of efficient solvers for SyGuS by providing a platform for evaluating different synthesis techniques on a comprehensive set of benchmarks. In this year's competition we added a new track devoted to programming by examples. This track consisted of two categories, one using the theory of bit-vectors and one using the theory of strings. This paper presents and analyses the results of SyGuS-Comp'16.Comment: In Proceedings SYNT 2016, arXiv:1611.07178. arXiv admin note: text overlap with arXiv:1602.0117