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31
Algorithmic Game Semantics
 In Schichtenberg and Steinbruggen [16
, 2001
"... Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntaxindependen ..."
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Cited by 70 (5 self)
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Introduction SAMSON ABRAMSKY (samson@comlab.ox.ac.uk) Oxford University Computing Laboratory 1. Introduction Game Semantics has emerged as a powerful paradigm for giving semantics to a variety of programming languages and logical systems. It has been used to construct the first syntaxindependent fully abstract models for a spectrum of programming languages ranging from purely functional languages to languages with nonfunctional features such as control operators and locallyscoped references [4, 21, 5, 19, 2, 22, 17, 11]. A substantial survey of the state of the art of Game Semantics circa 1997 was given in a previous Marktoberdorf volume [6]. Our aim in this tutorial presentation is to give a first indication of how Game Semantics can be developed in a new, algorithmic direction, with a view to applications in computerassisted verification and program analysis. Some promising steps have already been taken in this
Collapsible Pushdown Automata and Recursion Schemes
 23RD ANNUAL IEEE SYMPOSIUM ON LOGIC IN COMPUTER SCIENCE
, 2008
"... Collapsible pushdown automata (CPDA) are a new kind of higherorder pushdown automata in which every symbol in the stack has a link to a stack situated somewhere below it. In addition to the higherorder stack operations push i and pop i, CPDA have an important operation called collapse, whose effec ..."
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Cited by 52 (16 self)
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Collapsible pushdown automata (CPDA) are a new kind of higherorder pushdown automata in which every symbol in the stack has a link to a stack situated somewhere below it. In addition to the higherorder stack operations push i and pop i, CPDA have an important operation called collapse, whose effect is to “collapse ” a stack s to the prefix as indicated by the link from the topmost symbol of s. Our first result is that CPDA are equiexpressive with recursion schemes as generators of (possibly infinite) ranked trees. In one direction, we give a simple algorithm that transforms an ordern CPDA to an ordern recursion scheme that generates the same tree, uniformly for all n ≥ 0. In the other direction, using ideas from game semantics, we give an effective transformation of ordern recursion schemes (not assumed
A type system equivalent to the modal mucalculus model checking of higherorder recursion schemes
 IN: PROCEEDINGS OF LICS
, 2009
"... The model checking of higherorder recursion schemes has important applications in the verification of higherorder programs. Ong has previously shown that the modal mucalculus model checking of trees generated by ordern recursion scheme is nEXPTIME complete, but his algorithm and its correctness ..."
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Cited by 40 (13 self)
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The model checking of higherorder recursion schemes has important applications in the verification of higherorder programs. Ong has previously shown that the modal mucalculus model checking of trees generated by ordern recursion scheme is nEXPTIME complete, but his algorithm and its correctness proof were rather complex. We give an alternative, typebased verification method: Given a modal mucalculus formula, we can construct a type system in which a recursion scheme is typable if, and only if, the (possibly infinite, ranked) tree generated by the scheme satisfies the formula. The model checking problem is thus reduced to a type checking problem. Our typebased approach yields a simple verification algorithm, and its correctness proof (constructed without recourse to game semantics) is comparatively easy to understand. Furthermore, the algorithm is polynomialtime in the size of the recursion scheme, assuming that the formula and the largest order and arity of nonterminals of the recursion scheme are fixed.
Not enough points is enough
 IN: COMPUTER SCIENCE LOGIC. VOLUME 4646 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2007
"... Models of the untyped λcalculus may be defined either as applicative structures satisfying a bunch of first order axioms, known as “λmodels”, or as (structures arising from) any reflexive object in a cartesian closed category (ccc, for brevity). These notions are tightly linked in the sense that: ..."
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Cited by 26 (13 self)
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Models of the untyped λcalculus may be defined either as applicative structures satisfying a bunch of first order axioms, known as “λmodels”, or as (structures arising from) any reflexive object in a cartesian closed category (ccc, for brevity). These notions are tightly linked in the sense that: given a λmodel A, one may define a ccc in which A (the carrier set) is a reflexive object; conversely, if U is a reflexive object in a ccc C, having enough points, then C ( , U) may be turned into a λmodel. It is well known that, if C does not have enough points, then the applicative structure C ( , U) is not a λmodel in general. This paper: (i) shows that this mismatch can be avoided by choosing appropriately the carrier set of the λmodel associated with U; (ii) provides an example of an extensional reflexive object D in a ccc without enough points: the Kleislicategory of the comonad “finite multisets ” on Rel; (iii) presents some algebraic properties of the λmodel associated with D by (i) which make it suitable for dealing with nondeterministic extensions of the untyped λcalculus.
Syntactic Control of Concurrency
, 2004
"... We consider a finitary procedural programming language (finite datatypes, no recursion) extended with parallel composition and binary semaphores. Having first shown that mayequivalence of secondorder open terms is undecidable we set out to find a framework in which decidability can be regained wi ..."
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Cited by 21 (9 self)
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We consider a finitary procedural programming language (finite datatypes, no recursion) extended with parallel composition and binary semaphores. Having first shown that mayequivalence of secondorder open terms is undecidable we set out to find a framework in which decidability can be regained with minimum loss of expressivity. To that end we define an annotated type system that controls the number of concurrent threads created by terms and give a fully abstract game semantics for the notion of equivalence induced by typable terms and contexts. Finally, we show that the semantics of all typable terms, at any order and in the presence of iteration, has a regularlanguage representation and thus the restricted observational equivalence is decidable.
On Automated Verification of Probabilistic Programs
"... Abstract. We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over finite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence c ..."
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Cited by 13 (6 self)
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Abstract. We introduce a simple procedural probabilistic programming language which is suitable for coding a wide variety of randomised algorithms and protocols. This language is interpreted over finite datatypes and has a decidable equivalence problem. We have implemented an automated equivalence checker, which we call apex, for this language, based on game semantics. We illustrate our approach with three nontrivial case studies: (i) Herman’s selfstabilisation algorithm; (ii) an analysis of the average shape of binary search trees obtained by certain sequences of random insertions and deletions; and (iii) the problem of anonymity in the Dining Cryptographers protocol. In particular, we record an exponential speedup in the latter over stateoftheart competing approaches. 1
Observational equivalence of 3rdorder Idealized Algol is decidable
 In Proceedings of LICS’02. IEEE
, 2002
"... We prove that observational equivalence of 3rdorder finitary Idealized Algol (IA) is decidable using Game Semantics. By modelling state explicitly in our games, we show that the denotation of a term M of this fragment of IA (built up from finite base types) is a compactly innocent strategywithst ..."
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Cited by 12 (3 self)
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We prove that observational equivalence of 3rdorder finitary Idealized Algol (IA) is decidable using Game Semantics. By modelling state explicitly in our games, we show that the denotation of a term M of this fragment of IA (built up from finite base types) is a compactly innocent strategywithstate i.e. the strategy is generated by a finite view function fM . Given any such fM , we construct a realtime deterministic pushdown automata (DPDA) that recognizes the complete plays of the knowingstrategy denotation of M . Since such plays characterize observational equivalence, and there is an algorithm for deciding whether any two DPDAs recognize the same language, we obtain a procedure for deciding observational equivalence of 3rdorder finitary IA. This algorithmic representation of program meanings, which is compositional, provides a foundation for modelchecking a wide range of behavioural properties of IA and other cognate programming languages. Another result concerns 2ndorder IA with recursion: we show that observational equivalence for this fragment is undecidable. 1
Evolving Games and Essential Nets for Affine Polymorphism
"... This paper presents a game model of Secondorder Intuitionistic Multiplicative Affine Logic (IMAL2). We extend Lamarche's essential nets to the secondorder ane setting and use them to show that the model is fully and faithfully complete. ..."
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Cited by 9 (0 self)
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This paper presents a game model of Secondorder Intuitionistic Multiplicative Affine Logic (IMAL2). We extend Lamarche's essential nets to the secondorder ane setting and use them to show that the model is fully and faithfully complete.
On sequential functionals of type 3
 Math. Structures Comput. Sci
, 2006
"... We show that the extensional ordering of the sequential functionals of pure type 3, e.g. as defined via game semantics [2, 4], is not cpoenriched. This shows that this model does not equal Milner’s [9] fully abstract model for P CF. 1 ..."
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We show that the extensional ordering of the sequential functionals of pure type 3, e.g. as defined via game semantics [2, 4], is not cpoenriched. This shows that this model does not equal Milner’s [9] fully abstract model for P CF. 1