5 research outputs found
Sized Types with Usages for Parallel Complexity of Pi-Calculus Processes
We address the problem of analysing the complexity of concurrent programs written in Pi-calculus. We are interested in parallel complexity, or span, understood as the execution time in a model with maximal parallelism. A type system for parallel complexity has been recently proposed by the first two authors but it is too imprecise for non-linear channels and cannot analyse some concurrent processes. Aiming for a more precise analysis, we design a type system which builds on the concepts of sized types and usages. The sized types allow us to parametrize the complexity by the size of inputs, and the usages allow us to achieve a kind of rely-guarantee reasoning on the timing each process communicates with its environment. We prove that our new type system soundly estimates the parallel complexity, and show through examples that it is often more precise than the previous type system of the first two authors
Sound approximate and asymptotic probabilistic bisimulations for PCTL
We tackle the problem of establishing the soundness of approximate
bisimilarity with respect to PCTL and its relaxed semantics. To this purpose,
we consider a notion of bisimilarity inspired by the one introduced by
Desharnais, Laviolette, and Tracol, and parametric with respect to an
approximation error , and to the depth of the observation along
traces. Essentially, our soundness theorem establishes that, when a state
satisfies a given formula up-to error and steps , and is
bisimilar to up-to error and enough steps, we prove that
also satisfies the formula up-to a suitable error and steps . The
new error is computed from , and the formula, and
only depends linearly on . We provide a detailed overview of our soundness
proof. We extend our bisimilarity notion to families of states, thus obtaining
an asymptotic equivalence on such families. We then consider an asymptotic
satisfaction relation for PCTL formulae, and prove that asymptotically
equivalent families of states asymptotically satisfy the same formulae
Causal computational complexity of distributed processes
This article studies the complexity of π-calculus processes with respect to the quantity of transitions caused by an incoming message. First, we propose a typing system for integrating Bellantoni and Cook's characterisation of polytime computable functions into Deng and Sangiorgi's typing system for termination. We then define computational complexity of distributed messages based on Degano and Priami's causal semantics, which identifies the dependency between interleaved transitions. Next, we apply a necessary syntactic flow analysis to typable processes to ensure a computational bound on the number of distributed messages. We prove that our analysis is decidable; sound in the sense that it guarantees that the total number of messages causally dependent of an input request received from the outside is bounded by a polynomial of the content of this request; and complete, meaning that each polynomial recursive function can be computed by a typable process
Programming Languages and Systems
This open access book constitutes the proceedings of the 30th European Symposium on Programming, ESOP 2021, which was held during March 27 until April 1, 2021, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2021. The conference was planned to take place in Luxembourg and changed to an online format due to the COVID-19 pandemic. The 24 papers included in this volume were carefully reviewed and selected from 79 submissions. They deal with fundamental issues in the specification, design, analysis, and implementation of programming languages and systems
On session types and polynomial time
We show how systems of session types can enforce interactions to take bounded time for all typable processes. The type system we propose is based on Lafont's soft linear logic and is strongly inspired by recent works about session types as intuitionistic linear logic formulas. Our main result is the existence, for every typable process, of a polynomial bound on the length of reduction sequences starting from it and on the size of its reducts