Luke Ong

University of Oxford, Department of Computer Science, Faculty Member

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Gualtiero Piccinini

University of Missouri-Columbia

Judith L Green

University of California, Santa Barbara

Steven Pinker

Harvard University

Na'ama Pat-El

The University of Texas at Austin

E. Wayne Ross

University of British Columbia

Armando Marques-Guedes

UNL - New University of Lisbon

Eitan Grossman

The Hebrew University of Jerusalem

Martin Haspelmath

Max Planck Institute for Evolutionary Anthropology

Fabio Cuzzolin

Oxford Brookes University

Roshan Chitrakar

Nepal College of Information Technology

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A traversal-based algorithm for higher-order model checking

Higher-order model checking - the model checking of trees generated by higher-order recursion sch... more Higher-order model checking - the model checking of trees generated by higher-order recursion schemes (HORS) - is a natural generalisation of finite-state and pushdown model checking. Recent work has shown that it can serve as a basis for software model checking for functional languages such as ML and Haskell. In this paper, we introduce higher-order recursion schemes with cases (HORSC), which extend HORS with a definition-by-cases construct (to express program branching based on data) and non-determinism (to express abstractions of behaviours). This paper is a study of the universal HORSC model checking problem for deterministic trivial automata: does the automaton accept every tree in the tree language generated by the given HORSC? We first characterise the model checking problem by an intersection type system extended with a carefully restricted form of union types. We then present an algorithm for deciding the model checking problem, which is based on the notion of traversals induced by the fully abstract game semantics of these schemes, but presented as a goal-directed construction of derivations in the intersection and union type system. We view HORSC model checking as a suitable backend engine for an approach to verifying functional programs. We have implemented the algorithm in a tool called TravMC, and demonstrated its effectiveness on a test suite of programs, including abstract models of functional programs obtained via an abstraction-refinement procedure from pattern-matching recursion schemes.

Model Checking Algol-Like Languages Using Game Semantics

We survey a recent development of Game Semantics in a new, algorithmic direction, with a view to ... more

Route Oscillations in I-BGP

Adapting innocent game models for the Böhm tree λ-theory

Theoretical Computer Science, 2003

We present a game model of the untyped λ-calculus, with equational theory equal to the Böhm tree ... more We present a game model of the untyped λ-calculus, with equational theory equal to the Böhm tree λ-theory , which is universal (i.e. every element of the model is definable by some term). This answers a question of Di Gianantonio, Franco and Honsell. We build on our earlier work, which uses the methods of innocent game semantics to develop a universal model inducing the maximal consistent sensible theory . To our knowledge these are the first syntax-independent universal models of the untyped λ-calculus.

Hierarchies of Infinite Structures Generated by Pushdown Automata and Recursion Schemes

Higher-order recursion schemes and higher-order pushdown automata are closely related methods for... more Higher-order recursion schemes and higher-order pushdown automata are closely related methods for generating infinite hierarchies of infinite structures. Subsuming well-known classes of models of computation, these rich hierarchies (of word languages, trees, and graphs respectively) have excellent model-checking properties. In this extended abstract, we survey recent expressivity and decidability results about these infinite structures.

A Saturation Method for the Modal Mu-Calculus with Backwards Modalities over Pushdown Systems

Computing Research Repository, 2010

We present an algorithm for computing directly the denotation of a modal µcalculus formula χ with... more We present an algorithm for computing directly the denotation of a modal µcalculus formula χ with backwards modalities over the configuration graph of a pushdown system. Our method gives the first extension of the saturation technique to the full modal µ-calculus with backwards modalities. Finite word automata are used to represent sets of pushdown configurations. Starting from an initial automaton, we perform a series of automaton manipulations which compute the denotation by recursion over the structure of the formula. We introduce notions of under-approximation (soundness) and over-approximation (completeness) that apply to automaton transitions rather than runs. Our algorithm is relatively simple and direct, and avoids an immediate exponential blow up.

Luke Ong

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