Algebraic Model Checking for Discrete Linear Dynamical Systems

Abstract Model checking infinite-state systems is one of the central challenges in automated verification. In this survey we focus on an important and fundamental subclass systems, namely discrete linear dynamical systems. While such are ubiquitous mathematics, physics, engineering, etc., present context our motivation stems from their relevance to formal analysis verification program loops, weighted automata, hybrid control amongst many others. Our main object study problem model temporal properties infinite orbit a system, principal contribution show that for rich class can be reduced certain classical decision problems recurrence sequences, notably Skolem Problem. This leads us discuss recent advances latter highlight prospects further progress charting algorithmic landscape sequences