Computing and Information Systems - Research Publications
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ItemNo Preview AvailableProgramming to Learn: Logic and Computation from a Programming Perspective(Association for Computing Machinery, 2022-07-07)Programming problems are commonly used as a learning and assessment activity for learning to program. We believe that programming problems can be effective for broader learning goals. In our large-enrolment course, we have designed special programming problems relevant to logic, discrete mathematics, and the theory of computation, and we have used them for formative and summative assessment. In this report, we reflect on our experience. We aim to leverage our students' programming backgrounds by offering a code-based formalism for our mathematical syllabus. We find we can translate many traditional questions into programming problems of a special kind - calling for 'programs' as simple as a single expression, such as a formula or automaton represented in code. A web-based platform enables self-paced learning with rapid contextual corrective feedback, and helps us scale summative assessment to the size of our cohort. We identify several barriers arising with our approach and discuss how we have attempted to negate them. We highlight the potential of programming problems as a digital learning activity even beyond a logic and computation course.
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ItemString Abstract Domains and Their Combination(SPRINGER INTERNATIONAL PUBLISHING AG, 2022)We survey recent developments in string static analysis, with an emphasis on how string abstract domains can be combined. The paper has formed the basis for an invited presentation given to LOPSTR 2021 and PPDP 2021.
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ItemLightweight Nontermination Inference with CHCs(SPRINGER INTERNATIONAL PUBLISHING AG, 2021)Non-termination is an unwanted program property (considered a bug) for some software systems, and a safety property for other systems. In either case, automated discovery of preconditions for non-termination is of interest. We introduce NtHorn, a fast lightweight non-termination analyser, able to deduce non-trivial sufficient conditions for non-termination. Using Constrained Horn Clauses (CHCs) as a vehicle, we show how established techniques for CHC program transformation and abstract interpretation can be exploited for the purpose of non-termination analysis. NtHorn is comparable in power to the state-of-the-art non-termination analysis tools, as measured on standard competition benchmark suites (consisting of integer manipulating programs), while typically solving problems an order of magnitude faster.
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ItemDisjunctive Interval Analysis(SPRINGER INTERNATIONAL PUBLISHING AG, 2021)We revisit disjunctive interval analysis based on the Boxes abstract domain. We propose the use of what we call range decision diagrams (RDDs) to implement Boxes, and we provide algorithms for the necessary RDD operations. RDDs tend to be more compact than the linear decision diagrams (LDDs) that have traditionally been used for Boxes. Representing information more directly, RDDs also allow for the implementation of more accurate abstract operations. This comes at no cost in terms of analysis efficiency, whether LDDs utilise dynamic variable ordering or not. RDD and LDD implementations are available in the Crab analyzer, and our experiments confirm that RDDs are well suited for disjunctive interval analysis.
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ItemTeaching Simple Constructive Proofs with Haskell Programs(OPEN PUBL ASSOC, 2022)In recent years we have explored using Haskell alongside a traditional mathematical formalism in our large-enrolment university course on topics including logic and formal languages, aiming to offer our students a programming perspective on these mathematical topics. We have found it possible to offer almost all formative and summative assessment through an interactive learning platform, using Haskell as a lingua franca for digital exercises across our broad syllabus. One of the hardest exercises to convert into this format are traditional written proofs conveying constructive arguments. In this paper we reflect on the digitisation of this kind of exercise. We share many examples of Haskell exercises designed to target similar skills to written proof exercises across topics in propositional logic and formal languages, discussing various aspects of the design of such exercises. We also catalogue a sample of student responses to such exercises. This discussion contributes to our broader exploration of programming problems as a flexible digital medium for learning and assessment.
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ItemAbstract Interpretation over Non-Lattice Abstract Domains(Springer, 2013)The classical theoretical framework for static analysis of programs is abstract interpretation. Much of the power and elegance of that framework rests on the assumption that an abstract domain is a lattice. Nonetheless, and for good reason, the literature on program analysis provides many examples of non-lattice domains, including non-convex numeric domains. The lack of domain structure, however, has negative consequences, both for the precision of program analysis and for the termination of standard Kleene iteration. In this paper we explore these consequences and present general remedies.
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ItemAbstract interpretation, symbolic execution and constraints(Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020)Abstract interpretation is a static analysis framework for sound over-approximation of all possible runtime states of a program. Symbolic execution is a framework for reachability analysis which tries to explore all possible execution paths of a program. A shared feature between abstract interpretation and symbolic execution is that each – implicitly or explicitly – maintains constraints during execution, in the form of invariants or path conditions. We investigate the relations between the worlds of abstract interpretation, symbolic execution and constraint solving, to expose potential synergies.
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ItemFour-Valued Reasoning and Cyclic Circuits(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2014-07-01)Allowing cycles in a logic circuit can be advantageous, for example, by reducing the number of gates required to implement a given Boolean function, or a set of functions. However, a cyclic circuit may easily be ill behaved. For instance, it may have some output wire oscillation instead of reaching a steady state. Propositional three-valued logic has long been used in tests for good behavior of cyclic circuits; a symbolic evaluation method known as ternary analysis provides one criterion for good behavior under certain assumptions about wire and gate delay. We revisit ternary analysis and argue for the use of four truth values. The fourth truth value allows for the distinction of undefined and underspecified behavior. Ability to under specify behavior is useful, because, in a quest for smaller circuits, an implementor can capitalize on degrees of freedom offered in the specification. Moreover, a fourth truth value is attractive because, rather than complicating (ternary) circuit analysis, it introduces a pleasant symmetry, in the form of contra-duality, as well as providing a convenient framework for manipulating specifications. We use this symmetry to provide fixed point results that clarify how two-, three-, and four-valued analyses are related, and to explain some observations about ternary analysis.
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ItemSynthesizing Optimal Switching Lattices(Association for Computing Machinery, 2014-11)The use of nanoscale technologies to create electronic devices has revived interest in the use of regular structures for defining complex logic functions. One such structure is the switching lattice, a two-dimensional lattice of four-terminal switches. We show how to directly construct switching lattices of polynomial size from arbitrary logic functions; we also show how to synthesize minimal-sized lattices by translating the problem to the satisfiability problem for a restricted class of quantified Boolean formulas. The synthesis method is an anytime algorithm that uses modern SAT solving technology and dichotomic search. It improves considerably on an earlier proposal for creating switching lattices for arbitrary logic functions.
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ItemA complete refinement procedure for regular separability of context-free languages(ELSEVIER SCIENCE BV, 2016-04-25)Often, when analyzing the behaviour of systems modelled as context-free languages, we wish to know if two languages overlap. To this end, we present a class of semi-decision procedures for regular separability of context-free languages, based on counter-example guided abstraction refinement. We propose two effective instances of this approach, one that is complete but relatively expensive, and one that is inexpensive and sound, but for which we do not have a completeness proof. The complete method will prove disjointness whenever the input languages are regularly separable. Both methods will terminate whenever the input languages overlap. We provide an experimental evaluation of these procedures, and demonstrate their practicality on a range of verification and language-theoretic instances.