Formal Reachability Research Articles

POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled Systems

POLAR-Express: Efficient and Precise Formal Reachability Analysis of Neural-Network Controlled Systems

Formal Reachability Analysis for Multi-Agent Reinforcement Learning Systems

Reachability analysis is one of the most basic and challenging problems in verification. We investigate this problem in multi-agent reinforcement learning (MARL) system by transforming the reachability analysis to decision-making problem tackled by mixed integer linear programming (MILP) solver Gurobi. We define syntax and semantics for multi-role strategy logic (mrSL) which is used to describe the reachability specification. The logic mrSL is a variant of SL to express properties, which provide a holistic perspective to describe reachability properties instead of specifying a specific agent reaches a certain state in the MARL system. And the algorithms to translate reachability property into MILP constraints are provided. A tool called MAReachAnalysis is introduced, which uses Gurobi to solve the corresponding reachability problem and evaluate it on the predator-prey task of multi-agent deep deterministic policy gradient (MADDPG) example, discussion of the experimental results obtained on a range of test cases.

On formal reachability analysis in networks with dynamic behavior

Recently, several researches have suggested an application of formal methods for identifying configuration errors, unveiling design problems and predicting network behavior. In this paper, we contribute to this research area by defining a method able to efficiently check reachability properties in dynamically routed networks. We define a notion of network state that captures different network conditions. Each network state represents a unique combination of link availability. The naive enumeration of network states leads quickly to intractability even for small networks as the number of possible combinations grows exponentially. Instead, we enumerate all available paths and, for each path, we search for state aggregation, in which this path is active.

On reachability over polynomial rings and a related genericity problem†

Abstract The formal reachability property for a pair of matrices (A, B) over the polynomial ring ℛ = R[d1..., dk] in k symbols with real coefficients is considered where A is n by n, B is n by m with integers m being fixed. Reachability is defined as the property that ImRscr;[A|B]= ℛn n where [A |B] = [B, AB,..., A n−1B] is the formal reachability matrix for the pair (A, B). This abstract property is first characterized by a numerical rank criterion over the field of complex numbers. Then it is shown that reachability is generic if and only if k < m. It is hoped that the results presented will stimulate further research on polynomial output feedback controllers' for the delay-differential and multidiscrete-type systems.

On correct procedure parameter transmission in higher programming languages

The paper starts with the observation that in ALGOL 60 no specifications for formal procedure parameters are prescribed, whereas ALGOL 68 demands complete specifications. As a consequence, no ALGOL 68 program accepted by the compiler can have wrong parameter transmissions at run time whereas ALGOL 60 programs may have them. The property of ALGOL 60 programs to have only correct parameter transmissions obviously is undecidable if all data, conditional statements, etc. have to be taken into consideration (Theorem 1) and it is unfair to demand that the compiler should decide that property by a finite process. Therefore, we investigate this question of decidability under a much fairer condition, namely without taking into consideration any data or conditions and by giving all procedure calls occurring in the same block equal rights (Section IV, p. 123). Even this fairer problem turns out to be algorithmically unsolvable, in general (Theorem 5), but it is solvable as soon as the programs do not have global formal procedure parameters (Theorem 3). Analogous answers can be given to the problems of formal equivalence of programs and of formal reachability, formal recursivity, and strong formal recursivity of procedures (Theorems 8---11). Procedures which are not strongly formally recursive have great importance in compilation techniques as is shown in Section X.