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Register a new userParallelism and Synchronization in an Infinitary Context (Long Version)
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Added by
Ugo Dal Lago
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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We study multitoken interaction machines in the context of a very expressive logical system with exponentials, fixpoints and synchronization. The advantage of such machines is to provide models in the style of the Geometry of Interaction, i.e., an interactive semantics which is close to low-level implementation. On the one hand, we prove that despite the inherent complexity of the framework, interaction is guaranteed to be deadlock free. On the other hand, the resulting logical system is powerful enough to embed PCF and to adequately model its behaviour, both when call-by-name and when call-by-value evaluation are considered. This is not the case for single-token stateless interactive machines.
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We graft synchronization onto Girards Geometry of Interaction in its most concrete form, namely token machines. This is realized by introducing proof-nets for SMLL, an extension of multiplicative linear logic with a specific construct modeling synchronization points, and of a multi-token abstract machine model for it. Interestingly, the correctness criterion ensures the absence of deadlocks along reduction and in the underlying machine, this way linking logical and operational properties.
The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and context-free properties by ensuring decidability and tractability in the combined setting. To this end we introduce two real-time linear temporal logics for specifying quantitative timing context-free requirements in a pointwise semantics setting: Event-Clock Nested Temporal Logic (ECNTL) and Nested Metric Temporal Logic (NMTL). The logic ECNTL is an extension of both the logic CARET (a context-free extension of standard LTL) and Event-Clock Temporal Logic (a tractable real-time logical framework related to the class of Event-Clock automata). We prove that satisfiability of ECNTL and visibly model-checking of Visibly Pushdown Timed Automata VPTA against ECNTL are decidable and EXPTIME-complete. The other proposed logic NMTL is a context-free extension of standard Metric Temporal Logic (MTL). It is well known that satisfiability of future MTL is undecidable when interpreted over infinite timed words but decidable over finite timed words. On the other hand, we show that by augmenting future MTL with future context-free temporal operators, the satisfiability problem turns out to be undecidable also for finite timed words. On the positive side, we devise a meaningful and decidable fragment of the logic NMTL which is expressively equivalent to ECNTL and for which satisfiability and visibly model-checking of VPTA are EXPTIME-complete.
Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes themselves higher-order? This paper gives an answer to this question, by first describing why higher-order cryptography is interesting as an object of study, then showing how the concept of probabilistic polynomial time algorithm can be generalized so as to encompass algorithms of order strictly higher than two, and finally proving some positive and negative results about the existence of higher-order cryptographic primitives, namely authentication schemes and pseudorandom functions.
The space complexity of functional programs is not well understood. In particular, traditional implementation techniques are tailored to time efficiency, and space efficiency induces time inefficiencies, as it prefers re-computing to saving. Girards geometry of interaction underlies an alternative approach based on the interaction abstract machine (IAM), claimed as space efficient in the literature. It has also been conjectured to provide a reasonable notion of space for the lambda-calculus, but such an important result seems to be elusive. In this paper we introduce a new intersection type system precisely measuring the space consumption of the IAM on the typed term. Intersection types have been repeatedly used to measure time, which they achieve by dropping idempotency, turning intersections into multisets. Here we show that the space consumption of the IAM is connected to a further structural modification, turning multisets into trees. Tree intersection types lead to a finer understanding of some space complexity results from the literature. They also shed new light on the conjecture about reasonable space: we show that the usual way of encoding Turing machines into the lambda calculus cannot be used to prove that the space of the IAM is a reasonable cost model.
We study the logic obtained by endowing the language of first-order arithmetic with second-order measure quantifiers. This new kind of quantification allows us to express that the argument formula is true in a certain portion of all possible interpretations of the quantified variable. We show that first-order arithmetic with measure quantifiers is capable of formalizing simple results from probability theory and, most importantly, of representing every recursive random function. Moreover, we introduce a realizability interpretation of this logic in which programs have access to an oracle from the Cantor space.
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