ASFIX · Abstract semantic frameworks for implicit complexity
FP6 — Marie Curie Actions (Human Resources and Mobility)
- Duration
- 2007-01-01 → 2007-12-31
- EU contribution
- €72,567
- Participants
- 1
- Scheme
- EIF
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Results in brief
Final Activity Report Summary - ASFIX (Abstract Semantic Frameworks for Implicit Complexity)
The research area this project can be ascribed to is theoretical computer science. In particular, it concerned implicit computational complexity and semantics, as described in the project proposal. The objective of the project was the design of a unifying abstract semantic framework for implicit computational complexity. Particular attention was given to semantic frameworks in the spirit of game semantics and geometry of interaction, since they were inherently capable of revealing the intensional properties of programs and proofs. During his stay in Paris, the fellow interacted with researchers working in the host institution, namely Olivier Laurent, Paul-André Mellies and Pierre-Louis Curien. This interaction led to the definition of a game-theoretical framework for multiplicative and exponential linear logic. In this framework, the complexity of normalisation of any proof could be read out of its interpretation. Noticeably, the process of measuring the complexity of any proof could be internalised in the semantics and the underlying logical system. The framework was designed based on the fellows previous work on context semantics, linear logic and computational complexity. On the other hand, the great skills and expertise of the host institution researchers in game semantics were absolutely vital during all project phases. A technical report was jointly written by the fellow and Olivier Laurent and an extended abstract was submitted to an international conference on logic in computer science.
Data: CORDIS, © European Union
Project objective
Implicit computational complexity studies theory and applications of machine-independent approaches to computational complexity, with particular emphasis on approaches based on mathematical logic. Although related one to the other, all the proposed systems have been studied with different, often unrelated methodologies, and few results are known about relative intentional expressive power. For example, it is not clear at all whether combining different systems into one language would break the correspondence to complexity classes. Similarly, it is not usually the case that a system can be extended with new features preserving its quantitative properties. What is needed, are some unifying semantic frameworks for the analysis of resource consumptions of programming languages and proof systems. Such frameworks should be powerful enough to capture a wide amount of systems and programming language, but simple enough to be useful in studying quantitative properties of programs and proofs.Abstract semantic framework s for implicit computational complexity will be investigated. Particular emphasis will be placed on approaches based on game semantics, geometry of interaction and coherence semantics. The major expected result is the definition of an abstract mathematical structure in which heterogeneous systems inside implicit computational complexity can be interpreted. Crucially, the model must be sufficiently rich to reflect the quantitative behaviour of the interpreted object, in contrast to usual denotational semantics. The investigation will proceed in two steps. First of all, game models and geometry of interaction models will be developed in such a way that a large class of subsystems of linear logic (including the so called light logics) can be interpreted, studied and compared. Secondly, the semantics is extended in order to model languages outside linear logic, starting from higher-order recursion.
Original text from CORDIS.
Participants
- UNIVERSITE PARIS 7 DENIS DIDEROT · PARISCoordinatorCity levelFrance
Links
Data: CORDIS, © European Union