The input-state linear horizon (ISLH) for a nonlinear discrete-time system is defined as the smallest number of time steps it takes the system input to appear nonlinearly in the state variable. In this paper, we employ the latter concept and show that the class of constraint admissible N-step affine state-feedback policies is equivalent to the associated class of constraint admissible disturban...

A parameterized concurrent system represents an in nite family (of nite state systems) parameterized by a recursively de ned type such as chains, trees. It is therefore natural to verify parameterized systems by inducting over this type. We employ a program transformation based proof methodology to automate such induction proofs. Our proof technique is geared to automate nested induction proofs...

A fundamental advantage of Petri net models is the possibility to automatically compute useful system invariants from syntax net. Classical techniques used for this are place invariants, P-components, siphons or traps. Recently, Bozga et al. have presented a novel technique parameterized verification safety properties systems with ring array architecture. They show that statement “for every ins...

We consider policy evaluation in infinite-horizon discounted Markov decision problems with continuous compact state and action spaces. reformulate this task as a compositional stochastic program function-valued variable that belongs to reproducing kernel Hilbert space (RKHS). approach problem via new functional generalization of quasi-gradient methods operating tandem sparse subspace projection...

Synthesis is the process of automatically constructing an implementation from a specification. In parameterized synthesis, we construct a single process such that the distributed system consisting of an arbitratry number of copies of the process satisfies a parameterized specification. In this paper, we present Party, a tool for parameterized synthesis from specifications in indexed linear temp...

We provide a framework for modular deenitions and implementations of programming language based on abstract state machines. It is based on composition mechanism of state transition systems. State transition systems abstract from the algebraic structure of the states of an abstract state machine and focus on the behavior of state transitions. Implementations are based of reenements of state tran...

We present a tutorial on verification of safety properties for parameterized systems. Such a system consists of an arbitrary number of processes; the aim is to prove correctness of the system regardless of the number of processes inside the system. First, we consider a class of parameterized systems whose behaviours can be captured exactly as Petri nets using counter abstraction. This allows an...