Incremental Temporal Logic Synthesis of Control Policies for Robots Interacting with Dynamic Agents

We consider the synthesis of control policies from temporal logic specifications for robots that interact with multiple dynamic environment agents. Each environment agent is modeled by a Markov chain whereas the robot is modeled by a finite transition system (in the deterministic case) or Markov decision process (in the stochastic case). Existing results in probabilistic verification are adapted to solve the synthesis problem. To partially address the state explosion issue, we propose an incremental approach where only a small subset of environment agents is incorporated in the synthesis procedure initially and more agents are successively added until we hit the constraints on computational resources. Our algorithm runs in an anytime fashion where the probability that the robot satisfies its specification increases as the algorithm progresses

Fatal Attractors in Parity Games: Building Blocks for Partial Solvers

Attractors in parity games are a technical device for solving "alternating" reachability of given node sets. A well known solver of parity games - Zielonka's algorithm - uses such attractor computations recursively. We here propose new forms of attractors that are monotone in that they are aware of specific static patterns of colors encountered in reaching a given node set in alternating fashion. Then we demonstrate how these new forms of attractors can be embedded within greatest fixed-point computations to design solvers of parity games that run in polynomial time but are partial in that they may not decide the winning status of all nodes in the input game. Experimental results show that our partial solvers completely solve benchmarks that were constructed to challenge existing full solvers. Our partial solvers also have encouraging run times in practice. For one partial solver we prove that its run-time is at most cubic in the number of nodes in the parity game, that its output game is independent of the order in which monotone attractors are computed, and that it solves all Buechi games and weak games. We then define and study a transformation that converts partial solvers into more precise partial solvers, and we prove that this transformation is sound under very reasonable conditions on the input partial solvers. Noting that one of our partial solvers meets these conditions, we apply its transformation on 1.6 million randomly generated games and so experimentally validate that the transformation can be very effective in increasing the precision of partial solvers

A Compositional Proof System for the Modal mu-Calculus

We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal mu-calculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal mu-calculus and combines it with techniques from work on local model checking. The proof system is sound for all processes and complete for a class of finite-state processes

A Compositional Proof System for the Modal mu-Calculus

We present a proof system for determining satisfaction betweenprocesses in a fairly general process algebra and assertions of the modal mu-calculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal mu-calculus and combines it with techniques from work on local model checking. The proof system is sound for all processes and complete for a class of finite-state processes

Evidence for Fixpoint Logic

For many modal logics, dedicated model checkers offer diagnostics (e.g., counterexamples) that help the user understand the result provided by the solver. Fixpoint logic offers a unifying framework in which such problems can be expressed and solved, but a drawback of this framework is that it lacks comprehensive diagnostics generation. We extend the framework with a notion of evidence, which can be specialized to obtain diagnostics for various model checking problems, behavioural equivalence and refinement checking problems. We demonstrate this by showing how our notion of evidence can be used to obtain diagnostics for the problem of deciding stuttering bisimilarity. Moreover, we show that our notion generalizes the existing notions of counterexample and witness for LTL and ACTL* model checking