Title:

Model checking infinitestate systems : generic and specific approaches

Model checking is a fullyautomatic formal verification method that has been extremely successful in validating and verifying safetycritical systems in the past three decades. In the past fifteen years, there has been a lot of work in extending many model checking algorithms over finitestate systems to finitely representable infinitestate systems. Unlike in the case of finite systems, decidability can easily become a problem in the case of infinitestate model checking. In this thesis, we present generic and specific techniques that can be used to derive decidability with nearoptimal computational complexity for various model checking problems over infinitestate systems. Generic techniques and specific techniques primarily differ in the way in which a decidability result is derived. Generic techniques is a “topdown” approach wherein we start with a Turingpowerful formalismfor infinitestate systems (in the sense of being able to generate the computation graphs of Turing machines up to isomorphisms), and then impose semantic restrictions whereby the desired model checking problem becomes decidable. In other words, to show that a subclass of the infinitestate systems that is generated by this formalism is decidable with respect to the model checking problem under consideration, we will simply have to prove that this subclass satisfies the semantic restriction. On the other hand, specific techniques is a “bottomup” approach in the sense that we restrict to a nonTuring powerful formalism of infinitestate systems at the outset. The main benefit of generic techniques is that they can be used as algorithmic metatheorems, i.e., they can give unified proofs of decidability of various model checking problems over infinitestate systems. Specific techniques are more flexible in the sense they can be used to derive decidability or optimal complexity when generic techniques fail. In the first part of the thesis, we adopt word/tree automatic transition systems as a generic formalism of infinitestate systems. Such formalisms can be used to generate many interesting classes of infinitestate systems that have been considered in the literature, e.g., the computation graphs of counter systems, Turing machines, pushdown systems, prefixrecognizable systems, regular groundtree rewrite systems, PAprocesses, order2 collapsible pushdown systems. Although the generality of these formalisms make most interesting model checking problems (even safety) undecidable, they are known to have nice closure and algorithmic properties. We use these nice properties to obtain several algorithmic metatheorems over word/tree automatic systems, e.g., for deriving decidability of various model checking problems including recurrent reachability, and Linear Temporal Logic (LTL) with complex fairness constraints. These algorithmic metatheorems can be used to uniformly prove decidability with optimal (or nearoptimal) complexity of various model checking problems over many classes of infinitestate systems that have been considered in the literature. In fact, many of these decidability/complexity results were not previously known in the literature. In the second part of the thesis, we study various model checking problems over subclasses of counter systems that were already known to be decidable. In particular, we consider reversalbounded counter systems (and their extensions with discrete clocks), onecounter processes, and networks of onecounter processes. We shall derive optimal complexity of various model checking problems including: model checking LTL, EFlogic, and firstorder logic with reachability relations (and restrictions thereof). In most cases, we obtain a single/double exponential reduction in the previously known upper bounds on the complexity of the problems.
