82 research outputs found
Three notes on the complexity of model checking fixpoint logic with chop
This paper analyses the complexity of model checking fixpoint logic with Chop – an extension of the
modal μ-calculus with a sequential composition operator. It uses two known game-based characterisations
to derive the following results: the combined model checking complexity as well as the data complexity
of FLC are EXPTIME-complete. This is already the case for its alternation-free fragment. The expression
complexity of FLC is trivially P-hard and limited from above by the complexity of solving a
parity game, i.e. in UP ∩ co-UP. For any fragment of fixed alternation depth, in particular alternation-
free formulas it is P-complete
Non-Deterministic Functions as Non-Deterministic Processes
We study encodings of the ?-calculus into the ?-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider ?^?_?, a new non-deterministic calculus in which intersection types control resources (terms); on the concurrent side, we consider ??, a ?-calculus in which non-determinism and failure rest upon a Curry-Howard correspondence between linear logic and session types. We present a typed encoding of ?^?_? into ?? and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-prone evaluation in ?^?_? via typed processes in ??. In particular, it shows how failures in sequential evaluation (absence/excess of resources) can be neatly codified as interaction protocols
Non-Deterministic Functions as Non-Deterministic Processes
We study encodings of the λ-calculus into the Ï€-calculus in the unexplored case of calculi with non-determinism and failures. On the sequential side, we consider λ^↯_⊕, a new non-deterministic calculus in which intersection types control resources (terms); on the concurrent side, we consider sÏ€, a Ï€-calculus in which non-determinism and failure rest upon a Curry-Howard correspondence between linear logic and session types. We present a typed encoding of λ^↯_⊕ into sÏ€ and establish its correctness. Our encoding precisely explains the interplay of non-deterministic and fail-prone evaluation in λ^↯_⊕ via typed processes in sÏ€. In particular, it shows how failures in sequential evaluation (absence/excess of resources) can be neatly codified as interactio
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