State Space Reduction by Proving Confluence

Confluence Reduction for Markov Automata

“…We write s − α,µ −− → s if there is an extended transition s − α → µ such that µ(s ) > 0. We use s − α → t to denote s − α → 1 t , and write s → t if there is at least one action α such that s − α → t. For this system, rate(s 2 , s 1 ) = 3 + 4 = 7, rate(s 2 ) = 7 + 2 = 9, and P s2 = µ such that µ(s 1 ) = 7 9 and µ(s 3 ) = 2 9 . There are two extended transitions from s 2 : s 2 − a → 1 s3 (also written as s 2 − a → s 3 ) and s 2 − χ(9)…”

“…1 Related work. Confluence reduction for process algebras was first introduced for non-probabilistic systems [7], and later for probabilistic automata [25]. Also, several types of partial order reduction (POR) have been defined, both for nonprobabilistic [26,21,16] and probabilistic systems [11,4,3].…”

Some Trends in Formal Methods Applications to Railway Signaling

“…Namely, the state space belonging to the interlocking system at this station is so large that new verification techniques had to be implemented for the µCRL toolset, to cope with such large state spaces. They are based on partial order reduction [13], distributed state space generation [9], and minimization of such a distributed state space [10][11][12].…”

Leader Election in Anonymous Rings: Franklin Goes Probabilistic

“…Next it is symbolically reduced by static analysis: constant propagation (replace provably constant parameters by their initial value) [24], and dead variable analysis (reset variables that are not used anymore to a default value). The number of states and transitions of the state space that have been generated in this way are presented as the "normal" strategy in Tables 2 and 3. For more efficient state space generation, we applied symbolic confluence reduction [10]. To this end, a theorem prover can be used to automatically detect and mark confluent τ 's, i.e.…”