Quadtrees as an Abstract Domain

Quadtrees have proved popular in computer graphics and spatial databases as a way of representing regions in two dimensional space. This hierarchical data-structure is flexible enough to support non-convex and even disconnected regions, therefore it is natural to ask whether this datastructure can form the basis of an abstract domain. This paper explores this question and suggests that quadtrees offer a new approach to weakly relational domains whilst their hierarchical structure naturally lends itself to representation with boolean functions

Abstract State Machines 1988-1998: Commented ASM Bibliography

An annotated bibliography of papers which deal with or use Abstract State Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm

Automatic Termination Analysis of Programs Containing Arithmetic Predicates

For logic programs with arithmetic predicates, showing termination is not easy, since the usual order for the integers is not well-founded. A new method, easily incorporated in the TermiLog system for automatic termination analysis, is presented for showing termination in this case. The method consists of the following steps: First, a finite abstract domain for representing the range of integers is deduced automatically. Based on this abstraction, abstract interpretation is applied to the program. The result is a finite number of atoms abstracting answers to queries which are used to extend the technique of query-mapping pairs. For each query-mapping pair that is potentially non-terminating, a bounded (integer-valued) termination function is guessed. If traversing the pair decreases the value of the termination function, then termination is established. Simple functions often suffice for each query-mapping pair, and that gives our approach an edge over the classical approach of using a single termination function for all loops, which must inevitably be more complicated and harder to guess automatically. It is worth noting that the termination of McCarthy's 91 function can be shown automatically using our method. In summary, the proposed approach is based on combining a finite abstraction of the integers with the technique of the query-mapping pairs, and is essentially capable of dividing a termination proof into several cases, such that a simple termination function suffices for each case. Consequently, the whole process of proving termination can be done automatically in the framework of TermiLog and similar systems.Comment: Appeared also in Electronic Notes in Computer Science vol. 3

Some observations on the logical foundations of inductive theorem proving

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a goal. Based on this model, we then analyze the following aspects: the choice of a proof shape, the choice of an induction rule and the language of the induction formula. In particular, using model-theoretic techniques, we clarify the relationship between notions of inductiveness that have been considered in the literature on automated inductive theorem proving. This is a corrected version of the paper arXiv:1704.01930v5 published originally on Nov.~16, 2017

Quantitative Verification: Formal Guarantees for Timeliness, Reliability and Performance

Computerised systems appear in almost all aspects of our daily lives, often in safety-critical scenarios such as embedded control systems in cars and aircraft or medical devices such as pacemakers and sensors. We are thus increasingly reliant on these systems working correctly, despite often operating in unpredictable or unreliable environments. Designers of such devices need ways to guarantee that they will operate in a reliable and efficient manner. Quantitative verification is a technique for analysing quantitative aspects of a system's design, such as timeliness, reliability or performance. It applies formal methods, based on a rigorous analysis of a mathematical model of the system, to automatically prove certain precisely specified properties, e.g. ``the airbag will always deploy within 20 milliseconds after a crash'' or ``the probability of both sensors failing simultaneously is less than 0.001''. The ability to formally guarantee quantitative properties of this kind is beneficial across a wide range of application domains. For example, in safety-critical systems, it may be essential to establish credible bounds on the probability with which certain failures or combinations of failures can occur. In embedded control systems, it is often important to comply with strict constraints on timing or resources. More generally, being able to derive guarantees on precisely specified levels of performance or efficiency is a valuable tool in the design of, for example, wireless networking protocols, robotic systems or power management algorithms, to name but a few. This report gives a short introduction to quantitative verification, focusing in particular on a widely used technique called model checking, and its generalisation to the analysis of quantitative aspects of a system such as timing, probabilistic behaviour or resource usage. The intended audience is industrial designers and developers of systems such as those highlighted above who could benefit from the application of quantitative verification,but lack expertise in formal verification or modelling

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context

Split-2 Bisimilarity has a Finite Axiomatization over CCS with<br> Hennessy&#39;s Merge

This note shows that split-2 bisimulation equivalence (also known as timed equivalence) affords a finite equational axiomatization over the process algebra obtained by adding an auxiliary operation proposed by Hennessy in 1981 to the recursion, relabelling and restriction free fragment of Milner's Calculus of Communicating Systems. Thus the addition of a single binary operation, viz. Hennessy's merge, is sufficient for the finite equational axiomatization of parallel composition modulo this non-interleaving equivalence. This result is in sharp contrast to a theorem previously obtained by the same authors to the effect that the same language is not finitely based modulo bisimulation equivalence

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat