TY - GEN

T1 - Making weighted containment feasible

T2 - 23rd International Conference on Concurrency Theory, CONCUR 2012

AU - Avni, Guy

AU - Kupferman, Orna

PY - 2012

Y1 - 2012

N2 - Weighted automata map input words to real numbers and are useful in reasoning about quantitative systems and specifications. The containment problem for weighted automata asks, given two weighted automata A and B, whether for all words w, the value that A assigns to w is less than or equal to the value B assigns to w. The problem is of great practical interest, yet is known to be undecidable. Efforts to approximate weighted containment by weighted variants of the simulation pre-order still have to cope with large state spaces. One of the leading approaches for coping with large state spaces is abstraction. We introduce an abstraction-refinement paradigm for weighted automata and show that it nicely combines with weighted simulation, giving rise to a feasible approach for the containment problem. The weighted-simulation pre-order we define is based on a quantitative two-player game, and the technical challenge in the setting origins from the fact the values that the automata assign to words are unbounded. The abstraction-refinement paradigm is based on under- and over-approximation of the automata, where approximation, and hence also the refinement steps, refer not only to the languages of the automata but also to the values they assign to words.

AB - Weighted automata map input words to real numbers and are useful in reasoning about quantitative systems and specifications. The containment problem for weighted automata asks, given two weighted automata A and B, whether for all words w, the value that A assigns to w is less than or equal to the value B assigns to w. The problem is of great practical interest, yet is known to be undecidable. Efforts to approximate weighted containment by weighted variants of the simulation pre-order still have to cope with large state spaces. One of the leading approaches for coping with large state spaces is abstraction. We introduce an abstraction-refinement paradigm for weighted automata and show that it nicely combines with weighted simulation, giving rise to a feasible approach for the containment problem. The weighted-simulation pre-order we define is based on a quantitative two-player game, and the technical challenge in the setting origins from the fact the values that the automata assign to words are unbounded. The abstraction-refinement paradigm is based on under- and over-approximation of the automata, where approximation, and hence also the refinement steps, refer not only to the languages of the automata but also to the values they assign to words.

UR - http://www.scopus.com/inward/record.url?scp=84866675228&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-32940-1_8

DO - 10.1007/978-3-642-32940-1_8

M3 - Conference contribution

AN - SCOPUS:84866675228

SN - 9783642329395

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 84

EP - 99

BT - Concurrency Theory - 23rd International Conference, CONCUR 2012, Proceedings

Y2 - 4 September 2012 through 7 September 2012

ER -