Operational Semantics, Interval Orders and Sequences of Antichains

Issue title: Application and Theory of Petri Nets and Concurrency: Special Issue of Selected Papers from Petri Nets 2018

Guest editors: Victor Khomenko, Jetty Kleijn, Wojciech Penczek and Olivier H. Roux

Article type: Research Article

Authors: Janicki, Ryszard^{a; *} | Koutny, Maciej^b

Affiliations: [a] Department of Computing and Software, McMaster University, Hamilton, Ontario, L8S 4K1 Canada. janicki@mcmaster.ca | [b] School of Computing, Newcastle University, Newcastle upon Tyne NE1 7RU, U.K. maciej.koutny@newcastle.ac.uk

Correspondence: [*] Address for correspondence: Department of Computing and Software, McMaster University, Hamilton, Ontario, L8S 4K1 Canada

Abstract: A representation of interval orders by sequences of antichains is discussed, and its relationship to the Fishburn’s representation by sequences of the beginnings and endings of domain elements is analysed in detail. Moreover, an operational semantics based on sequences of maximal antichains is proposed and investigated for a general class of safe Petri nets with context arcs.

Keywords: interval order, operational semantics, Petri net, sequence of maximal antichains, interval sequence

DOI: 10.3233/FI-2019-1838

Journal: Fundamenta Informaticae, vol. 169, no. 1-2, pp. 31-55, 2019