Leveraging Weighted Automata in Compositional Reasoning about Concurrent Probabilistic Systems

Abstract

We propose the first sound and complete learning-based compositional verification technique for probabilistic safety properties on concurrent systems where each component is an Markov decision process. Different from previous works, weighted assumptions are introduced to attain completeness of our framework. Since weighted assumptions can be implicitly represented by multi-terminal binary decision diagrams (MTBDD's), we give an L * -based learning algorithm for MTBDD's to infer weighted assumptions. Experimental results suggest promising outlooks for our compositional technique.

Compositional Stochastic Model Checking Probabilistic Automata via Assume-guarantee Reasoning

“…Bouchekir and Boukala [19], He et al [20], Komuravelli et al [21], Feng et al [22] and [23] are the automated assumption generation methods for solving the AG-SMC problem. They can be divided into the following three kinds further.…”

“…One deficiency of learning-based assumption generation method is that the learning framework is sound but incomplete. Based on ASYM rule, He et al [20] proposes an assume-guarantee rule containing weighted assumption for the first time, and provides a sound and complete learning framework, which can verify whether the probabilistic safety properties are satisfied on the MDP model. Through randomized consensus algorithm, wireless LAN protocol, FireWire protocol and randomized dining philosophers, He et al [20] demonstrates the performance of its method.…”

“…Based on ASYM rule, He et al [20] proposes an assume-guarantee rule containing weighted assumption for the first time, and provides a sound and complete learning framework, which can verify whether the probabilistic safety properties are satisfied on the MDP model. Through randomized consensus algorithm, wireless LAN protocol, FireWire protocol and randomized dining philosophers, He et al [20] demonstrates the performance of its method. For the AG-CSMC problem, He et al [20] can be specifically described in the following four aspects: (1) The weighted assumption can be represented by Multi-terminal Binary Decision Diagrams (MTBDD).…”

“…Through randomized consensus algorithm, wireless LAN protocol, FireWire protocol and randomized dining philosophers, He et al [20] demonstrates the performance of its method. For the AG-CSMC problem, He et al [20] can be specifically described in the following four aspects: (1) The weighted assumption can be represented by Multi-terminal Binary Decision Diagrams (MTBDD). Based on the L* learning algorithm, He et al [20] proposes an MTBDD learning algorithm to automatically generate the weighted assumption, which is represented by a k-Deterministic Finite Automaton (k-DFA).…”

“…For the AG-CSMC problem, He et al [20] can be specifically described in the following four aspects: (1) The weighted assumption can be represented by Multi-terminal Binary Decision Diagrams (MTBDD). Based on the L* learning algorithm, He et al [20] proposes an MTBDD learning algorithm to automatically generate the weighted assumption, which is represented by a k-Deterministic Finite Automaton (k-DFA). MTBDD learning algorithm can make membership queries on binary strings of arbitrary lengths and answer membership queries on valuations over fixed variables by the teacher.…”