An Axiomatic Approach to Reversible Computation

Undoing computations of a concurrent system is beneficial inmany situations, e.g., in reversible debugging of multi-threaded programsand in recovery from errors due to optimistic execution in parallel dis-crete event simulation. A number of approaches have been proposed forhow to reverse formal models of concurrent computation including pro-cess calculi such as CCS, languages like Erlang, prime eventstructuresand occurrence nets. However it has not been settled what properties areversible system should enjoy, nor how the various properties that havebeen suggested, such as the parabolic lemma and the causal-consistencyproperty, are related. We contribute to a solution to these issues by usinga generic labelled transition system equipped with a relationcapturingwhether transitions are independent to explore the implications betweenthese properties. In particular, we show how they are derivable from aset of axioms. Our intention is that when establishing properties of someformalism it will be easier to verify the axioms rather than proving prop-erties such as the parabolic lemma directly. We also introduce two newnotions related to causal consistent reversibility, namely causal safetyand causal liveness, and show that they are derivable from our axioms

Bridging Causal Reversibility and Time Reversibility: A Stochastic Process Algebraic Approach

Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a past consistent state. Time reversibility is instead considered in the field of stochastic processes, mostly for efficient analysis purposes. A performance model based on a continuous-time Markov chain is time reversible if its stochastic behavior remains the same when the direction of time is reversed. We bridge these two theories of reversibility by showing the conditions under which causal reversibility and time reversibility are both ensured by construction. This is done in the setting of a stochastic process calculus, which is then equipped with a variant of stochastic bisimilarity accounting for both forward and backward directions

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

Enabling Replications and Contexts in Reversible Concurrent Calculus

Existing formalisms for the algebraic specification and representation of networks of reversible agents suffer some shortcomings. Despite multiple attempts, reversible declensions of the Calculus of Communicating Systems (CCS) do not offer satisfactory adaptation of notions that are usual in "forward-only" process algebras, such as replication or context. They also seem to fail to leverage possible new features stemming from reversibility, such as the capacity of distinguishing between multiple replications, based on how they replicate the memory mechanism allowing to reverse the computation. Existing formalisms disallow the "hot-plugging" of processes during their execution in contexts that also have a past. Finally, they assume the existence of "eternally fresh" keys or identifiers that, if implemented poorly, could result in unnecessary bottlenecks and look-ups involving all the threads. In this paper, we begin investigating those issues, by first designing a process algebra endowed with a mechanism to generate identifiers without the need to consult with the other threads. We use this calculus to recast the possible representations of non-determinism in CCS, and as a by-product establish a simple and straightforward definition of concurrency. Our reversible calculus is then proven to satisfy expected properties, and allows to lay out precisely different representations of the replication of a process with a memory. We also observe that none of the reversible bisimulations defined thus far are congruences under our notion of "reversible" contexts

Bridging Causal Reversibility and Time Reversibility: A Stochastic Process Algebraic Approach

Causal reversibility blends reversibility and causality for concurrent systems. It indicates that an action can be undone provided that all of its consequences have been undone already, thus making it possible to bring the system back to a past consistent state. Time reversibility is instead considered in the field of stochastic processes, mostly for efficient analysis purposes. A performance model based on a continuous-time Markov chain is time reversible if its stochastic behavior remains the same when the direction of time is reversed. We bridge these two theories of reversibility by showing the conditions under which causal reversibility and time reversibility are both ensured by construction. This is done in the setting of a stochastic process calculus, which is then equipped with a variant of stochastic bisimilarity accounting for both forward and backward directions

Foundations of Software Science and Computation Structures

This open access book constitutes the proceedings of the 23rd International Conference on Foundations of Software Science and Computational Structures, FOSSACS 2020, which took place in Dublin, Ireland, in April 2020, and was held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2020. The 31 regular papers presented in this volume were carefully reviewed and selected from 98 submissions. The papers cover topics such as categorical models and logics; language theory, automata, and games; modal, spatial, and temporal logics; type theory and proof theory; concurrency theory and process calculi; rewriting theory; semantics of programming languages; program analysis, correctness, transformation, and verification; logics of programming; software specification and refinement; models of concurrent, reactive, stochastic, distributed, hybrid, and mobile systems; emerging models of computation; logical aspects of computational complexity; models of software security; and logical foundations of data bases.

An axiomatic approach to reversible computation

Undoing computations of a concurrent system is beneficial inmany situations, e.g., in reversible debugging of multi-threaded programsand in recovery from errors due to optimistic execution in parallel dis-crete event simulation. A number of approaches have been proposed forhow to reverse formal models of concurrent computation including pro-cess calculi such as CCS, languages like Erlang, prime eventstructuresand occurrence nets. However it has not been settled what properties areversible system should enjoy, nor how the various properties that havebeen suggested, such as the parabolic lemma and the causal-consistencyproperty, are related. We contribute to a solution to these issues by usinga generic labelled transition system equipped with a relationcapturingwhether transitions are independent to explore the implications betweenthese properties. In particular, we show how they are derivable from aset of axioms. Our intention is that when establishing properties of someformalism it will be easier to verify the axioms rather than proving prop-erties such as the parabolic lemma directly. We also introduce two newnotions related to causal consistent reversibility, namely causal safetyand causal liveness, and show that they are derivable from our axioms