7 research outputs found
Game semantic analysis of equivalence in IMJ
Using game semantics, we investigate the problem of verifying contextual equivalences in Interface Middleweight Java (IMJ), an imperative object calculus in which program phrases are typed using interfaces. Working in the setting where data types are non-recursive and restricted to finite domains, we identify the frontier between decidability and undecidability by reference to the structure of interfaces present in typing judgments. In particular, we show how to determine the decidability status of problem instances (over a fixed type signature) by examining the position of methods inside the term type and the types of its free identifiers. Our results build upon the recent fully abstract game semantics of IMJ. Decidability is proved by translation into visibly pushdown register automata over infinite alphabets with fresh-input recognition
History-Register Automata
Programs with dynamic allocation are able to create and use an unbounded
number of fresh resources, such as references, objects, files, etc. We propose
History-Register Automata (HRA), a new automata-theoretic formalism for
modelling such programs. HRAs extend the expressiveness of previous approaches
and bring us to the limits of decidability for reachability checks. The
distinctive feature of our machines is their use of unbounded memory sets
(histories) where input symbols can be selectively stored and compared with
symbols to follow. In addition, stored symbols can be consumed or deleted by
reset. We show that the combination of consumption and reset capabilities
renders the automata powerful enough to imitate counter machines, and yields
closure under all regular operations apart from complementation. We moreover
examine weaker notions of HRAs which strike different balances between
expressiveness and effectiveness.Comment: LMCS (improved version of FoSSaCS
Saturating automata for game semantics
Saturation is a fundamental game-semantic property satisfied by strategies
that interpret higher-order concurrent programs. It states that the strategy
must be closed under certain rearrangements of moves, and corresponds to the
intuition that program moves (P-moves) may depend only on moves made by the
environment (O-moves).
We propose an automata model over an infinite alphabet, called saturating
automata, for which all accepted languages are guaranteed to satisfy a closure
property mimicking saturation.
We show how to translate the finitary fragment of Idealized Concurrent Algol
(FICA) into saturating automata, confirming their suitability for modelling
higher-order concurrency. Moreover, we find that, for terms in normal form, the
resultant automaton has linearly many transitions and states with respect to
term size, and can be constructed in polynomial time. This is in contrast to
earlier attempts at finding automata-theoretic models of FICA, which did not
guarantee saturation and involved an exponential blow-up during translation,
even for normal forms.Comment: Presented at MFPS 202
Game Semantics for Interface Middleweight Java
We consider an object calculus in which open terms interact with the environment through interfaces. The calculus is intended to capture the essence of contextual interactions of Middleweight Java code. Using game semantics, we provide fully abstract models for the induced notions of contextual approximation and equivalence. These are the first denotational models of this kind
Reachability in pushdown register automata
We investigate reachability in pushdown automata over infinite alphabets. We show that, in terms of reachability/emptiness,
these machines can be faithfully represented using only 3r elements of the alphabet, where r is the number of registers. We settle the complexity of associated reachability/emptiness problems. In contrast to register automata, the emptiness problem for pushdown register automata is EXPTIME-complete, independent of the register
storage policy used. We also solve the global reachability problem by representing pushdown configurations with a special register automaton. Finally, we examine extensions of pushdown storage to higher orders and show that reachability is undecidable at order 2