Moment Semantics for Reversible Rule-Based Systems

International audienceWe develop a notion of stochastic rewriting over marked graphs – i.e. directed multigraphs with degree constraints. The approach is based on double-pushout (DPO) graph rewriting. Marked graphs are expressive enough to internalize the 'no-dangling-edge' condition inherent in DPO rewriting. Our main result is that the linear span of marked graph occurrence-counting functions – or motif functions – form an algebra which is closed under the infinitesimal generator of (the Markov chain associated with) any such rewriting system. This gives a general procedure to derive the moment semantics of any such rewriting system, as a countable (and recursively enumerable) system of differential equations indexed by motif functions. The differential system describes the time evolution of moments (of any order) of these motif functions under the rewriting system. We illustrate the semantics using the example of preferential attachment networks; a well-studied complex system, which meshes well with our notion of marked graph rewriting. We show how in this case our procedure obtains a finite description of all moments of degree counts for a fixed degree

Reversing Single Sessions

Session-based communication has gained a widespread acceptance in practice as a means for developing safe communicating systems via structured interactions. In this paper, we investigate how these structured interactions are affected by reversibility, which provides a computational model allowing executed interactions to be undone. In particular, we provide a systematic study of the integration of different notions of reversibility in both binary and multiparty single sessions. The considered forms of reversibility are: one for completely reversing a given session with one backward step, and another for also restoring any intermediate state of the session with either one backward step or multiple ones. We analyse the costs of reversing a session in all these different settings. Our results show that extending binary single sessions to multiparty ones does not affect the reversibility machinery and its costs

A General Approach to Derive Uncontrolled Reversible Semantics

Reversible computing is a paradigm where programs can execute backward as well as in the usual forward direction. Reversible computing is attracting interest due to its applications in areas as different as biochemical modelling, simulation, robotics and debugging, among others. In concurrent systems the main notion of reversible computing is called causal-consistent reversibility, and it allows one to undo an action if and only if its consequences, if any, have already been undone. This paper presents a general and automatic technique to define a causal-consistent reversible extension for given forward models. We support models defined using a reduction semantics in a specific format and consider a causality relation based on resources consumed and produced. The considered format is general enough to fit many formalisms studied in the literature on causal-consistent reversibility, notably Higher-Order ?-calculus and Core Erlang, an intermediate language in the Erlang compilation. Reversible extensions of these models in the literature are ad hoc, while we build them using the same general technique. This also allows us to show in a uniform way that a number of relevant properties, causal-consistency in particular, hold in the reversible extensions we build. Our technique also allows us to go beyond the reversible models in the literature: we cover a larger fragment of Core Erlang, including remote error handling based on links, which has never been considered in the reversibility literature

A general approach to derive uncontrolled reversible semantics

Reversible computing is a paradigm where programs can execute backward as well as in the usual forward direction. Reversible computing is attracting interest due to its applications in areas as different as biochemical modelling, simulation, robotics and debugging, among others. In concurrent systems the main notion of reversible computing is called causal-consistent reversibility, and it allows one to undo an action if and only if its consequences, if any, have already been undone. This paper presents a general and automatic technique to define a causal-consistent reversible extension for given forward models. We support models defined using a reduction semantics in a specific format and consider a causality relation based on resources consumed and produced. The considered format is general enough to fit many formalisms studied in the literature on causal-consistent reversibility, notably Higher-Order π-calculus and Core Erlang, an intermediate language in the Erlang compilation. Reversible extensions of these models in the literature are ad hoc, while we build them using the same general technique. This also allows us to show in a uniform way that a number of relevant properties, causal-consistency in particular, hold in the reversible extensions we build. Our technique also allows us to go beyond the reversible models in the literature: we cover a larger fragment of Core Erlang, including remote error handling based on links, which has never been considered in the reversibility literature

Inadequacy of Modal Logic in Quantum Settings

We test the principles of classical modal logic in fully quantum settings. Modal logic models our reasoning in multi-agent problems, and allows us to solve puzzles like the muddy children paradox. The Frauchiger-Renner thought experiment highlighted fundamental problems in applying classical reasoning when quantum agents are involved; we take it as a guiding example to test the axioms of classical modal logic. In doing so, we find a problem in the original formulation of the Frauchiger-Renner theorem: a missing assumption about unitarity of evolution is necessary to derive a contradiction and prove the theorem. Adding this assumption clarifies how different interpretations of quantum theory fit in, i.e., which properties they violate. Finally, we show how most of the axioms of classical modal logic break down in quantum settings, and attempt to generalize them. Namely, we introduce constructions of trust and context, which highlight the importance of an exact structure of trust relations between agents. We propose a challenge to the community: to find conditions for the validity of trust relations, strong enough to exorcise the paradox and weak enough to still recover classical logic.Comment: In Proceedings QPL 2018, arXiv:1901.0947

Thermodynamic graph-rewriting

We develop a new thermodynamic approach to stochastic graph-rewriting. The ingredients are a finite set of reversible graph-rewriting rules called generating rules, a finite set of connected graphs P called energy patterns and an energy cost function. The idea is that the generators define the qualitative dynamics, by showing which transformations are possible, while the energy patterns and cost function specify the long-term probability $\pi$ of any reachable graph. Given the generators and energy patterns, we construct a finite set of rules which (i) has the same qualitative transition system as the generators; and (ii) when equipped with suitable rates, defines a continuous-time Markov chain of which $\pi$ is the unique fixed point. The construction relies on the use of site graphs and a technique of `growth policy' for quantitative rule refinement which is of independent interest. This division of labour between the qualitative and long-term quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the examples in S4 and S5). It also guarantees thermodynamical consistency (AKA detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications

Systems Biology Markup Language (SBML) Level 2: Structures and Facilities for Model Definitions

With the rise of Systems Biology as a new paradigm for understanding biological processes, the development of quantitative models is no longer restricted to a small circle of theoreticians. The dramatic increase in the number of these models precipitates the need to exchange and reuse both existing and newly created models. The Systems Biology Markup Language (SBML) is a free, open, XML-based format for representing quantitative models of biological interest that advocates the consistent specification of such models and thus facilitates both software development and model exchange.

Principally oriented towards describing systems of biochemical reactions, such as cell signalling pathways, metabolic networks and gene regulation etc., SBML can also be used to encode any kinetic model. SBML offers mechanisms to describe biological components by means of compartments and reacting species, as well as their dynamic behaviour, using reactions, events and arbitrary mathematical rules. SBML also offers all the housekeeping structures needed to ensure an unambiguous understanding of quantitative descriptions.

This is Release 1 of the specification for SBML Level 2 Version 4, describing the structures of the language and the rules used to build a valid model. SBML XML Schema and other related documents and software are also available from the SBML project web site, "http://sbml.org/":http://sbml.org/

Robust Grammatical Analysis for Spoken Dialogue Systems

We argue that grammatical analysis is a viable alternative to concept spotting for processing spoken input in a practical spoken dialogue system. We discuss the structure of the grammar, and a model for robust parsing which combines linguistic sources of information and statistical sources of information. We discuss test results suggesting that grammatical processing allows fast and accurate processing of spoken input.Comment: Accepted for JNL