The Power of Priority Channel Systems

• Published in: Logical methods in computer science Vol. 10, Issue 4; no. 4:4; pp. 1 - 39
• Main Authors: Haase, Christoph, Schmitz, Sylvain, Schnoebelen, Philippe
• Format: Journal Article
• Language: English
• Published: Logical Methods in Computer Science Association 03.12.2014; Logical Methods in Computer Science e.V
• Subjects: Computer Science; computer science - logic in computer science; Logic in Computer Science; Well quasi order; well-structured transition systems; fast-growing complexity
• ISSN: 1860-5974; 1860-5974
• DOI: 10.2168/LMCS-10(4:4)2014

We introduce Priority Channel Systems, a new class of channel systems where messages carry a numeric priority and where higher-priority messages can supersede lower-priority messages preceding them in the fifo communication buffers. The decidability of safety and inevitability properties is shown via the introduction of a priority embedding, a well-quasi-ordering that has not previously been used in well-structured systems. We then show how Priority Channel Systems can compute Fast-Growing functions and prove that the aforementioned verification problems are $\mathbf{F}_{\varepsilon_{0}}$-complete.