Synthesis and Control of Infinite-State Systems with Partial Observability
Complex computer systems play an important role in every part of everyday life and their correctness is often vital to human safety. In light of the recent advances in the area of formal methods and the increasing availability and maturity of tools and techniques, the use of verification techniques to show that a system satisfies a specified property is about to become an integral part of the development process. To minimize the development costs, formal methods must be applied as early as possible, before the entire system is fully developed, or even at the stage when only its specification is available. The goal of synthesis is to automatically construct an implementation guaranteed to fulfill the provided specification, and, if no implementation exists, to report that the given requirements cannot be realized. When synthesizing an individual component within a system and its external environment, the synthesis procedure must take into account the component’s interface and deliver implementations that comply with it. For example, what a component can observe about its environment may be restricted by imprecise sensors or inaccessible communication channels. In addition, sufficiently precise models of a component’s environment are typically infinite-state, for example due to modeling real time or unbounded communication buffers. This thesis presents novel synthesis methods that respect the given interface limitations of the synthesized system components and are applicable to infinite-state models.
The studied computational model is that of infinite-state two-player games under incomplete information. The contributions are structured into three parts, corresponding to a classification of such games according to the interface between the synthesized component and its environment. In the first part, we obtain decidability results for a class of game structures where the player corresponding to the synthesized component has a given finite set of possible observations and a finite set of possible actions. A prominent type of systems for which the interface of a component naturally defines a finite set of observations are Lossy Channel Systems. We provide symbolic game solving and strategy synthesis algorithms for lossy channel games under incomplete information with safety and reachability winning conditions. Our second contribution is a counterexample-guided abstraction refinement scheme for solving infinite-state under incomplete information in which the actions available to the component are still finitely many, but no finite set of possible observations is given. This situation is common, for example, in the synthesis of mutex protocols or robot controllers. In this setting, the observations correspond to observation predicates, which are logical formulas, and their computation is an integral part of our synthesis procedure. The resulting game solving method is applicable to games that are out of the scope of other available techniques. Last we study systems in which, in addition to the possibly infinite set of observation predicates, the component can choose between infinitely many possible actions. Timed games under incomplete information are a fundamental class of games for which this is the case. We extend the abstraction-refinement procedure to develop the first systematic method for the synthesis of observation predicates for timed control. Automatically refining the set of candidate observations based on counterexamples demonstrates better potential than brute-force enumeration of observation sets, in particular for systems where fine granularity of the observations is necessary.