Strategy representation and reasoning has received much attention over the past years. In this paper, we consider the representation of general strategies that solve a class of (possibly infinitely many) games with similar structures, and their automatic verification, which is an undecidable problem. We propose to represent a general strategy by an FSA (Finite State Automaton) with edges labelled by restricted Golog programs. We formalize the semantics of FSA strategies in the situation calculus. Then we propose an incomplete method for verifying whether an FSA strategy is a winning strategy by counterexample-guided local search for appropriate invariants. We implemented our method and did experiments on combinatorial game and also single-agent domains. Experimental results showed that our system can successfully verify most of them within a reasonable amount of time.
Generalized planning aims at finding a general solution for a set of similar planning problems. Abstractions are widely used to solve such problems. However, the connections among these abstraction works remain vague. Thus, to facilitate a deep understanding and further exploration of abstraction approaches for generalized planning, it is important to develop a uniform abstraction framework for generalized planning. Recently, Banihashemi et al. proposed an agent abstraction framework based on the situation calculus. However, expressiveness of such an abstraction framework is limited. In this paper, by extending their abstraction framework, we propose a uniform abstraction framework for generalized planning. We formalize a generalized planning problem as a triple of a basic action theory, a trajectory constraint, and a goal. Then we define the concepts of sound abstractions of a generalized planning problem. We show that solutions to a generalized planning problem are nicely related to those of its sound abstractions. We also define and analyze the dual notion of complete abstractions. Finally, we review some important abstraction works for generalized planning and show that they can be formalized in our framework.
Abstraction has long been an effective mechanism to help find a solution in classical planning. Agent abstraction, based on the situation calculus, is a promising explainable framework for agent planning, yet its automation is still far from being tackled. In this paper, we focus on a propositional version of agent abstraction designed for finite-state systems. We investigate the automated verification of the existence of propositional agent abstraction, given a finite-state system and a mapping indicating an abstraction for it. By formalizing sound, complete and deterministic properties of abstractions in a general framework, we show that the verification task can be reduced to the task of model checking against CTLK specifications. We implemented a prototype system, and validated the viability of our approach through experimentation on several domains from classical planning.
Strategy synthesis for multi-agent systems has proved to be a hard task, even when limited to two-player games with safety objectives. Generalized strategy synthesis, an extension of generalized planning which aims to produce a single solution for multiple (possibly infinitely many) planning instances, is a promising direction to deal with the state-space explosion problem. In this paper, we formalize the problem of generalized strategy synthesis in the situation calculus. The synthesis task involves second-order theorem proving generally. Thus we consider strategies aiming to maintain invariants; such strategies can be verified with first-order theorem proving. We propose a sound but incomplete approach to synthesize invariant strategies by adapting the framework of counterexample-guided refinement. The key idea for refinement is to generate a strategy using a model checker for a game constructed from the counterexample, and use it to refine the candidate general strategy. We implemented our method and did experiments with a number of game problems. Our system can successfully synthesize solutions for most of the domains within a reasonable amount of time.
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