The Design of CoCoALib

Probabilistic reachability for parametric Markov models

“…We implemented methods and data structures to handle rational functions for example the basic arithmetic operations, comparisons and simplification. The computer algebra library CoCoALib [1] is used for handling the cancellation part. For details of the tool, we refer to the corresponding tool paper [15].…”

“…We let D 1 = (S 1 , s 0 , P 1 ) denote the PMC before elimination of the state s ∈ S \ B ∪ {s 0 }, and let D 2 = (S 2 , s 0 , P 2 ) denote the PMC after eliminating state s. Assume that u is maximal welldefined for D 1 . By construction of the algorithm, it holds that S 2 = S 1 \ {s}, and that…”

PARAM: A Model Checker for Parametric Markov Models

“…The prototype of PARAM relied on data structures provided by the arithmetic library CoCoALib [12]. PARAM 1.0 instead uses dedicated data structures and a novel, memory-efficient implementation of rational functions, to avoid costly conversions between PARAM and CoCoALib.…”

Probabilistic Reachability for Parametric Markov Models

“…For PMDP, bisimulation is run for the encoded PMC. We use the computer algebra library CoCoALib [1] for handling arithmetic of rational functions, for example the basic arithmetic operations, comparisons and simplification.…”

“…P(s n−1 , s n ) + P(sn−1,s)P(s,sn) For (1), the transition probability is P 1 (s j , s j+1 ), as we have a direct transition from s j to s j+1 at this point. For (2), we first have a transition from s j to s, then a number of i j − 1 self-loops in s and then a transition from s to s j+1 , leading to a probability of P 1 (s j , s)P 1 (s, s) ij −1 P 1 (s, s j+1 ).…”