Kaiser, Lukasz ;
Leßenich, Simon
A Counting Logic for Structure Transition Systems
Abstract
Quantitative questions such as "what is the maximum number of tokens
in a place of a Petri net?" or "what is the maximal reachable height
of the stack of a pushdown automaton?" play a significant role in
understanding models of computation. To study such problems in a
systematic way, we introduce structure transition systems on which
one can define logics that mix temporal expressions (e.g. reachability) with properties of a state (e.g. the height of the stack). We propose a counting logic Qmu[#MSO] which allows to express questions like the ones above, and also many boundedness problems studied so far. We show that Qmu[#MSO] has good algorithmic properties, in particular we generalize two standard methods in model checking, decomposition on trees and model checking through parity games, to this quantitative logic. These properties are used to prove decidability of Qmu[#MSO] on treeproducing pushdown systems, a generalization of both pushdown systems and regular tree grammars.
BibTeX  Entry
@InProceedings{kaiser_et_al:LIPIcs:2012:3684,
author = {Lukasz Kaiser and Simon Le{\ss}enich},
title = {{A Counting Logic for Structure Transition Systems}},
booktitle = {Computer Science Logic (CSL'12)  26th International Workshop/21st Annual Conference of the EACSL},
pages = {366380},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {9783939897422},
ISSN = {18688969},
year = {2012},
volume = {16},
editor = {Patrick C{\'e}gielski and Arnaud Durand},
publisher = {Schloss DagstuhlLeibnizZentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2012/3684},
URN = {urn:nbn:de:0030drops36848},
doi = {10.4230/LIPIcs.CSL.2012.366},
annote = {Keywords: Logic in Computer Science, Quantitative Logics, Model Checking}
}
2012
Keywords: 

Logic in Computer Science, Quantitative Logics, Model Checking 
Seminar: 

Computer Science Logic (CSL'12)  26th International Workshop/21st Annual Conference of the EACSL

Issue date: 

2012 
Date of publication: 

2012 