Buffered Simulation Games for B\"uchi Automata

Simulation relations are an important tool in automata theory because they provide efficiently computable approximations to language inclusion. In recent years, extensions of ordinary simulations have been studied, for instance multi-pebble and multi-letter simulations which yield better approximations and are still polynomial-time computable. In this paper we study the limitations of approximating language inclusion in this way: we introduce a natural extension of multi-letter simulations called buffered simulations. They are based on a simulation game in which the two players share a FIFO buffer of unbounded size. We consider two variants of these buffered games called continuous and look-ahead simulation which differ in how elements can be removed from the FIFO buffer. We show that look-ahead simulation, the simpler one, is already PSPACE-hard, i.e. computationally as hard as language inclusion itself. Continuous simulation is even EXPTIME-hard. We also provide matching upper bounds for solving these games with infinite state spaces.Comment: In Proceedings AFL 2014, arXiv:1405.527

Cuts for circular proofs: semantics and cut-elimination

One of the authors introduced in [Santocanale, FoSSaCS, 2002] a calculus of circular proofs for studying the computability arising from the following categorical operations: finite products, finite coproducts, initial algebras, final coalgebras. The calculus presented [Santocanale, FoSSaCS, 2002] is cut-free; even if sound and complete for provability, it lacked an important property for the semantics of proofs, namely fullness w.r.t. the class of intended categorical models (called mu-bicomplete categories in [Santocanale, ITA, 2002]). In this paper we fix this problem by adding the cut rule to the calculus and by modifying accordingly the syntactical constraint ensuring soundness of proofs. The enhanced proof system fully represents arrows of the canonical model (a free mu-bicomplete category). We also describe a cut-elimination procedure as a a model of computation arising from the above mentioned categorical operations. The procedure constructs a cut-free proof-tree with possibly infinite branches out of a finite circular proof with cuts

An Infinitary Proof Theory of Linear Logic Ensuring Fair Termination in the Linear ?-Calculus

Fair termination is the property of programs that may diverge "in principle" but that terminate "in practice", i.e. under suitable fairness assumptions concerning the resolution of non-deterministic choices. We study a conservative extension of ?MALL^?, the infinitary proof system of the multiplicative additive fragment of linear logic with least and greatest fixed points, such that cut elimination corresponds to fair termination. Proof terms are processes of ?LIN, a variant of the linear ?-calculus with (co)recursive types into which binary and (some) multiparty sessions can be encoded. As a result we obtain a behavioral type system for ?LIN (and indirectly for session calculi through their encoding into ?LIN) that ensures fair termination: although well-typed processes may engage in arbitrarily long interactions, they are fairly guaranteed to eventually perform all pending actions

Ain't No Stopping Us Monitoring Now

Not all properties are monitorable. This is a well-known fact, and it means there exist properties that cannot be fully verified at runtime. However, given a non-monitorable property, a monitor can still be synthesised, but it could end up in a state where no verdict will ever be concluded on the satisfaction (resp., violation) of the property. For this reason, non-monitorable properties are usually discarded. In this paper, we carry out an in-depth analysis on monitorability, and how non-monitorable properties can still be partially verified. We present our theoretical results at a semantic level, without focusing on a specific formalism. Then, we show how our theory can be applied to achieve partial runtime verification of Linear Temporal Logic (LTL)

A Tableau Proof System with Names for Modal Mu-calculus

Fixpoints are an important ingredient in semantics, abstract interpretation and program logics. Their addition to a logic can add considerable expressive power. One general issue is how to define proof systems for such logics. Here we examine proof systems for modal logic with fixpoints. We present a tableau proof system for checking validity of formulas which uses names to keep track of unfoldings of fixpoint variables as devised by Jungteerapanich

Infinitary cut-elimination via finite approximations

We investigate non-wellfounded proof systems based on parsimonious logic, a weaker variant of linear logic where the exponential modality ! is interpreted as a constructor for streams over finite data. Logical consistency is maintained at a global level by adapting a standard progressing criterion. We present an infinitary version of cut-elimination based on finite approximations, and we prove that, in presence of the progressing criterion, it returns well-defined non-wellfounded proofs at its limit. Furthermore, we show that cut-elimination preserves the progressive criterion and various regularity conditions internalizing degrees of proof-theoretical uniformity. Finally, we provide a denotational semantics for our systems based on the relational model