Faster Algorithms for Alternating Refinement Relations
One central issue in the formal design and analysis of reactive systems is the notion of refinement that asks whether all behaviors of the implementation is allowed by the specification. The local interpretation of behavior leads to the notion of simulation. Alternating transition systems (ATSs) provide a general model for composite reactive systems, and the simulation relation for ATSs is known as alternating simulation. The simulation relation for fair transition systems is called fair simulation. In this work our main contributions are as follows: (1) We present an improved algorithm for fair simulation with Büchi fairness constraints; our algorithm requires O(n^3 * m) time as compared to the previous known O(n^6)-time algorithm, where n is the number of states and m is the number of transitions. (2) We present a game based algorithm for alternating simulation that requires O(m^2)-time as compared to the previous known O((n*m)^2)-time algorithm, where n is the number of states and m is the size of transition relation. (3) We present an iterative algorithm for alternating simulation that matches the time complexity of the game based algorithm, but is more space efficient than the game based algorithm.
Simulation and fair simulation
Alternating simulation
Graph games
167-182
Regular Paper
Krishnendu
Chatterjee
Krishnendu Chatterjee
Siddhesh
Chaubal
Siddhesh Chaubal
Pritish
Kamath
Pritish Kamath
10.4230/LIPIcs.CSL.2012.167
Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported license
https://creativecommons.org/licenses/by-nc-nd/3.0/legalcode