## Mennicke, Roy - Propositional Dynamic Logic with Converse and Repeat for Message-Passing Systems

lmcs:855 - Logical Methods in Computer Science, June 28, 2013, Volume 9, Issue 2
Propositional Dynamic Logic with Converse and Repeat for Message-Passing Systems

Authors: Mennicke, Roy

The model checking problem for propositional dynamic logic (PDL) over message sequence charts (MSCs) and communicating finite state machines (CFMs) asks, given a channel bound $B$, a PDL formula $\varphi$ and a CFM $\mathcal{C}$, whether every existentially $B$-bounded MSC $M$ accepted by $\mathcal{C}$ satisfies $\varphi$. Recently, it was shown that this problem is PSPACE-complete. In the present work, we consider CRPDL over MSCs which is PDL equipped with the operators converse and repeat. The former enables one to walk back and forth within an MSC using a single path expression whereas the latter allows to express that a path expression can be repeated infinitely often. To solve the model checking problem for this logic, we define message sequence chart automata (MSCAs) which are multi-way alternating parity automata walking on MSCs. By exploiting a new concept called concatenation states, we are able to inductively construct, for every CRPDL formula $\varphi$, an MSCA precisely accepting the set of models of $\varphi$. As a result, we obtain that the model checking problem for CRPDL and CFMs is still in PSPACE.

Source : oai:arXiv.org:1306.3059
DOI : 10.2168/LMCS-9(2:12)2013
Volume: Volume 9, Issue 2
Published on: June 28, 2013
Submitted on: December 21, 2012
Keywords: Computer Science - Logic in Computer Science