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Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are able to capture the notions of causality and simultaneity of atomic actions which take place during the process of a systems operation. The aim of this paper is a transfer to the domain of comtraces and developing of some fundamental notions, which proved to be successful in the theory of traces. In particular, we introduce and then apply the notion of indivisible steps, the lexicographical canonical form of comtraces, as well as the representation of a comtrace utilising its linear projections to binary action subalphabets. We also provide two algorithms related to the new notions. Using them, one can solve, in an efficient way, the problem of step sequence equivalence in the context of comtraces. One may view our results as a first step towards the development of infinite combined traces, as well as recognisable languages of combined traces.
In the theory of coalgebras, trace semantics can be defined in various distinct ways, including through algebraic logics, the Kleisli category of a monad or its Eilenberg-Moore category. This paper elaborates two new unifying ideas: 1) coalgebraic tr
Five algebraic notions of termination are formalised, analysed and compared: wellfoundedness or Noetherity, Lobs formula, absence of infinite iteration, absence of divergence and normalisation. The study is based on modal semirings, which are additiv
This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 Algebraic effect handlers go mainstream. It is targeted roughly at the level of a d
In this paper, we settle a problem in probabilistic verification of infinite--state process (specifically, {it probabilistic pushdown process}). We show that model checking {it stateless probabilistic pushdown process} (pBPA) against {it probabilistic computational tree logic} (PCTL) is undecidable.
In this paper, we investigate the module-checking problem of pushdown multi-agent systems (PMS) against ATL and ATL* specifications. We establish that for ATL, module checking of PMS is 2EXPTIME-complete, which is the same complexity as pushdown modu