An Efficient Synthesis Algorithm for Parametric Markov Chains Against Linear Time Properties

TL;DR

This paper introduces a linear-complexity algorithm for parameter synthesis in parametric Markov chains against linear time properties, utilizing automata translation and SMT solving for efficient verification.

Contribution

It presents a novel, efficient algorithm that reduces the synthesis problem to an SMT optimization, applicable to interval Markov chains and with linear complexity in chain size.

Findings

Algorithm is efficient on benchmark problems.

Works for interval Markov chains.

Complexity is linear in chain size, exponential in formula size.

Abstract

In this paper, we propose an efficient algorithm for the parameter synthesis of PLTL formulas with respect to parametric Markov chains. The PLTL formula is translated to an almost fully partitioned B\"uchi automaton which is then composed with the parametric Markov chain. We then reduce the problem to solving an optimisation problem, allowing to decide the satisfaction of the formula using an SMT solver. The algorithm works also for interval Markov chains. The complexity is linear in the size of the Markov chain, and exponential in the size of the formula. We provide a prototype and show the efficiency of our approach on a number of benchmarks.