A regular viewpoint on processes and algebra

While different algebraic structures have been proposed for the treatment of concurrency, finding solutions for equations over these structures needs to be worked on further. This article is a survey of process algebra from a very narrow viewpoint, that of finite automata and regular languages. What have automata theorists learnt from process algebra about finite state concurrency? The title is stolen from [31]. There is a recent survey article [7] on finite state processes which deals extensively with rational expressions. The aim of the present article is different. How do standard notions such as Petri nets, Mazurkiewicz trace languages and Zielonka automata fare in the world of process algebra? This article has no original results, and the attempt is to raise questions rather than answer them

Modelchecking counting properties of 1-safe nets with buffers in paraPSPACE

We consider concurrent systems that can be modelled as $1$-safe Petri nets communicating through a fixed set of buffers (modelled as unbounded places). We identify a parameter $ben$, which we call ``benefit depth\u27\u27, formed from the communication graph between the buffers. We show that for our system model, the coverability and boundedness problems can be solved in polynomial space assuming $ben$ to be a fixed parameter, that is, the space requirement is $f(ben)p(n)$, where $f$ is an exponential function and $p$ is a polynomial in the size of the input. We then obtain similar complexity bounds for modelchecking a logic based on such counting properties. This means that systems that have sparse communication patterns can be analyzed more efficiently than using previously known algorithms for general Petri nets

Agent-update Models

In dynamic epistemic logic (Van Ditmarsch et al., 2008) it is customary to use an action frame (Baltag and Moss, 2004; Baltag et al., 1998) to describe different views of a single action. In this article, action frames are extended to add or remove agents, we call these agent-update frames. This can be done selectively so that only some specified agents get information of the update, which can be used to model several interesting examples such as private update and deception, studied earlier by Baltag and Moss (2004); Sakama (2015); Van Ditmarsch et al. (2012). The product update of a Kripke model by an action frame is an abbreviated way of describing the transformed Kripke model which is the result of performing the action. This is substantially extended to a sum-product update of a Kripke model by an agent-update frame in the new setting. These ideas are applied to an AI problem of modelling a story. We show that dynamic epistemic logics, with update modalities now based on agent-update frames, continue to have sound and complete proof systems. Decision procedures for model checking and satisfiability have expected complexity. A sublanguage is shown to have polynomial space algorithms

An Algebraic Decision Procedure for Two-Variable Logic with a Between Relation

In earlier work (LICS 2016), the authors introduced two-variable first-order logic supplemented by a binary relation that allows one to say that a letter appears between two positions. We found an effective algebraic criterion that is a necessary condition for definability in this logic, and conjectured that the criterion is also sufficient, although we proved this only in the case of two-letter alphabets. Here we prove the general conjecture. The proof is quite different from the arguments in the earlier work, and required the development of novel techniques concerning factorizations of words. We extend the results to binary relations specifying that a factor appears between two positions

COVID-19 : symptoms and spread

What symptoms does one experience if they have COVID-19? How long does it take to recover from infection? When is hospitalization likely to be necessary? Can asymptomatic people spread the infection? What precautions help minimize the risks of transmitting the infection