Feasible reactivity in a synchronous pi-calculus

Reactivity is an essential property of a synchronous program. Informally, it guarantees that at each instant the program fed with an input will `react' producing an output. In the present work, we consider a refined property that we call ` feasible reactivity'. Beyond reactivity, this property guarantees that at each instant both the size of the program and its reaction time are bounded by a polynomial in the size of the parameters at the beginning of the computation and the size of the largest input. We propose a method to annotate programs and we develop related static analysis techniques that guarantee feasible reactivity for programs expressed in the S-pi-calculus. The latter is a synchronous version of the pi-calculus based on the SL synchronous programming model

Complexity Information Flow in a Multi-threaded Imperative Language

We propose a type system to analyze the time consumed by multi-threaded imperative programs with a shared global memory, which delineates a class of safe multi-threaded programs. We demonstrate that a safe multi-threaded program runs in polynomial time if (i) it is strongly terminating wrt a non-deterministic scheduling policy or (ii) it terminates wrt a deterministic and quiet scheduling policy. As a consequence, we also characterize the set of polynomial time functions. The type system presented is based on the fundamental notion of data tiering, which is central in implicit computational complexity. It regulates the information flow in a computation. This aspect is interesting in that the type system bears a resemblance to typed based information flow analysis and notions of non-interference. As far as we know, this is the first characterization by a type system of polynomial time multi-threaded programs

Safe Reactive Programming: The FunLoft Proposal

We propose a multicore-ready programming language based on a two-level shared memory model. Concurrency units are schedulers and threads which are dispatched on available cores in a preemptive way. Each scheduler is in charge of its own portion of the memory. At runtime, several threads may link to a common scheduler. In this case, they enter a cooperative mode, evolve in synchronous rounds, and are granted access to the scheduler memory. At the opposite, an autonomous thread runs at its own pace but has access only to a local memory. The language ensures that programs are free of memory leaks, that code between two cooperation points is atomic, and that rounds are fair and always terminate (no run-time error nor divergence)

Determinacy in a synchronous pi-calculus

To appear in the book `From semantics to computer science: essays in honor of Gilles Kahn', Cambridge University Press.The S-pi-calculus is a synchronous pi-calculus which is based on the SL model. The latter is a relaxation of the Esterel model where the reaction to the absence of a signal within an instant can only happen at the next instant. In the present work, we present and characterise a compositional semantics of the S-pi-calculus based on suitable notions of labelled transition system and bisimulation. Based on this semantic framework, we explore the notion of determinacy and the related one of (local) confluence

The SL synchronous language, revisited

International audienceWe revisit the SL synchronous programming model introduced by Boussinot and De Simone (IEEE, Trans. on Soft. Eng., 1996). We discuss an alternative design of the model including thread spawning and recursive definitions and we explore some basic properties of the revised model: determinism, reactivity, CPS translation to a tail recursive form, computational expressivity, and a compositional notion of program equivalence

On stratified regions

Type and effect systems are a tool to analyse statically the behaviour of programs with effects. We present a proof based on the so called reducibility candidates that a suitable stratification of the type and effect system entails the termination of the typable programs. The proof technique covers a simply typed, multi-threaded, call-by-value lambda-calculus, equipped with a variety of scheduling (preemptive, cooperative) and interaction mechanisms (references, channels, signals)

Formalisation of FunLoft

We formalise a thread-based concurrent language which makes resource control possible. Concurrency is based on a two-level model: threads are executed cooperatively when linked to a scheduler, and unlinked threads and schedulers are executed preemptively, under the control of the OS. We present a type and effect system to enforce a logical separation of the memory which ensures that (1) when running in preemptive mode, threads do not interfere with other threads; (2) threads linked to a scheduler do not interfere with threads linked to another scheduler. Thus, we get a concurrency model in which well-typed programs are free from data-races. The type system also insures that well-typed programs are bounded in memory and in their use of the CPU. Detection of termination of recursive functions and stratification of references in memory are techniques used to get these properties

Type-based complexity analysis for fork processes

International audienceWe introduce a type system for concurrent programs described as a parallel imperative language using while-loops and fork/wait instructions, in which processes do not share a global memory, in order to analyze computational complexity. The type system provides an analysis of the data-flow based both on a data ramification principle related to tiering discipline and on secure typed languages. The main result states that well-typed processes characterize exactly the set of functions computable in polynomial space under termination, confluence and lock-freedom assumptions. More precisely, each process computes in polynomial time so that the evaluation of a process may be performed in polynomial time on a parallel model of computation. Type inference of the presented analysis is decidable in linear time provided that basic operator semantics is known

Complexity Information Flow in a Multi-threaded Imperative Language

International audienceWe propose a type system to analyze the time consumed by multi-threaded imperative programs with a shared global memory, which delineates a class of safe multi-threaded programs. We demon-strate that a safe multi-threaded program runs in polynomial time if (i) it is strongly terminating wrt a non-deterministic scheduling policy or (ii) it terminates wrt a deterministic and quiet scheduling policy. As a consequence, we also characterize the set of polynomial time functions. The type system presented is based on the fundamental notion of data tiering, which is central in implicit computational complexity. It regu-lates the information flow in a computation. This aspect is interesting in that the type system bears a resemblance to typed based informa-tion flow analysis and notions of non-interference. As far as we know, this is the first characterization by a type system of polynomial time multi-threaded programs