This work discusses the reachability analysis (RA) of Max-Plus Linear (MPL) systems, a class of continuous-space, discrete-event models defined over the max-plus algebra. Given the initial and target sets, we develop algorithms to verify whether there exist trajectories of the MPL system that, starting from the initial set, eventually reach the target set. We show that RA can be solved symbolically by encoding the MPL system, as well as initial and target sets into difference logic, and then checking the satisfaction of the resulting logical formula via an off-the-shelf satisfiability modulo theories (SMT) solver. The performance and scalability of the developed SMT-based algorithms are shown to clearly outperform state-of-the-art RA algorithms for MPL systems, newly allowing to investigate RA of high-dimensional MPL systems: the verification of models with more than 100 continuous variables shows the applicability of these techniques to MPL systems of industrial relevance.
Weighted timed automata have been defined in the early 2000's for modelling resource-consumption or -allocation problems in real-time systems. Optimal reachability is decidable in weighted timed automata, and a symbolic forward algorithm has been developed to solve that problem. This algorithm uses so-called priced zones, an extension of standard zones with cost functions. In order to ensure termination, the algorithm requires clocks to be bounded. For unpriced timed automata, much work has been done to develop sound abstractions adapted to the forward exploration of timed automata, ensuring t…
We consider the problem of symbolic reachability analysis of higher-order context-free processes. These models are generalizations of the context-free processes (also called BPA processes) where each process manipulates a data structure which can be seen as a nested stack of stacks. Our main result is that, for any higher-order context-free process, the set of all predecessors of a given regular set of configurations is regular and effectively constructible. This result generalizes the analogous result which is known for level 1 context-free processes. We show that this result holds also in th…
We present an approach to parameterized reachability for communicating finite-state threads that formulates the analysis as a satisfiability problem. In addition to the unbounded number of threads, the main challenge for SAT/SMT-based reachability methods is the existence of unbounded loops in the program executed by a thread. We show in this paper how simple loops can be accelerated without approximation into Presburger arithmetic constraints. The constraints are obtained via symbolic execution and are satisfiable exactly if the given program state is reachable. We summarize loops nested insi…
IC3 has been a leap forward in symbolic model checking. This paper proposes PrIC3 (pronounced pricy-three), a conservative extension of IC3 to symbolic model checking of MDPs. Our main focus is to develop the theory underlying PrIC3. Alongside, we present a first implementation of PrIC3 including the key ingredients from IC3 such as generalization, repushing, and propagation.
There is a scalability gap between probabilistic and non-probabilistic verification. Probabilistic model checking tools are based either on explicit engines or on (Multi-Terminal) Binary Decision Diagrams. These structures are complemented in areas of non-probabilistic verification by more scalable techniques, such as IC3. We present a symbolic probabilistic model checking algorithm based on IC3-like incremental construction of inductive clauses to partition the state space, interleaved with incremental construction of a system of linear inequalities. This paper compares our implementation to …
Since the introduction of Alternating-time Temporal Logic (ATL), many logics have been proposed to reason about different strategic capabilities of the agents of a system. In particular, some logics have been designed to reason about the uniform memoryless strategies of such agents. These strategies are the ones the agents can effectively play by only looking at what they observe from the current state. ATL_ir can be seen as the core logic to reason about such uniform strategies. Nevertheless, its model-checking problem is difficult (it requires a polynomial number of calls to an NP oracle), a…
The timed automata formalism is an important model for specifying and analysing real-time systems. Robustness is the correctness of the model in the presence of small drifts on clocks or imprecision in testing guards. A symbolic algorithm for the analysis of the robustness of timed automata has been implemented. In this paper, we re-analyse an industrial case lip synchronization protocol using the new robust reachability algorithm. This lip synchronization protocol is an interesting case because timing aspects are crucial for the correctness of the protocol. Several versions of the model are c…
In this work, we consider the fundamental problem of reachability analysis over imperative programs with real variables. The reachability property requires that a program can reach certain target states during its execution. Previous works that tackle reachability analysis are either unable to handle programs consisting of general loops (e.g. symbolic execution), or lack completeness guarantees (e.g. abstract interpretation), or are not automated (e.g. incorrectness logic/reverse Hoare logic). In contrast, we propose a novel approach for reachability analysis that can handle general programs, …
TTT: A Temporal Refinement Heuristic for Tenuously Tractable Discrete Time Reachability Problems
Division of Robotics, Perception and Learning, Intelligent Systems Department, School of Electrical Engineering & Computer Science（机器人、感知与学习 division，智能系统部门，电气工程与计算机科学学院）；Digital Futures at KTH Royal Institute of Technology（KTH皇家理工学院数字未来）
The goal of the thesis is to leverage fast graph algorithms and modern algorithmic techniques for problems in model checking and synthesis on graphs, MDPs, and game graphs. The results include symbolic algorithms, a well-known class of algorithms in model checking that trades limited access to the input model for an efficient representation. In particular, we present the following results: Algorithms for game graphs with mean-payoff Büchi objectives and mean-payoff coBüchi objectives which match one of the best running time bounds for mean-payoff objectives. A near-linear time randomized algor…
In a reachability-time game, players Min and Max choose moves so that the time to reach a final state in a timed automaton is minimised or maximised, respectively. Asarin and Maler showed decidability of reachability-time games on strongly non-Zeno timed automata using a value iteration algorithm. This paper complements their work by providing a strategy improvement algorithm for the problem. It also generalizes their decidability result because the proposed strategy improvement algorithm solves reachability-time games on all timed automata. The exact computational complexity of solving reacha…
Reconfigurable broadcast networks (RBN) are a model of distributed computation in which agents can broadcast messages to other agents using some underlying communication topology which can change arbitrarily over the course of executions. In this paper, we conduct parameterized analysis of RBN. We consider cubes,(infinite) sets of configurations in the form of lower and upper bounds on the number of agents in each state, and we show that we can evaluate boolean combinations over cubes and reachability sets of cubes in PSPACE. In particular, reachability from a cube to another cube is a PSPACE-…
We consider concurrent games played on graphs. At every round of a game, each player simultaneously and independently selects a move; the moves jointly determine the transition to a successor state. Two basic objectives are the safety objective to stay forever in a given set of states, and its dual, the reachability objective to reach a given set of states. We present in this paper a strategy improvement algorithm for computing the value of a concurrent safety game, that is, the maximal probability with which player~1 can enforce the safety objective. The algorithm yields a sequence of player-…
We propose two parallel state-space exploration algorithms for hybrid systems with the goal of enhancing performance on multi-core shared memory systems. The first is an adaption of the parallel breadth first search in the SPIN model checker. We show that the adapted algorithm does not provide the desired load balancing for many hybrid systems benchmarks. The second is a task parallel algorithm based on cheaply precomputing cost of post (continuous and discrete) operations for effective load balancing. We illustrate the task parallel algorithm and the cost precomputation of post operators on a…
