Hierarchic decision procedures for verification

Information-handling systems are becoming ever more complex. They may be pure hardware or software systems, or complex systems of hardware and software that act in a real-world environment. Verification is a method to ensure that systems behave in the expected way, which is a necessity for safety-critical applications like automatic railway control. The size of such systems makes manual verification impossible. Therefore, we need automatic or computer-aided verification procedures. Automated reasoning is already widely used in the analysis and verification of systems. For a restricted class of systems, the resulting verification problems are inherently finite and can be solved efficiently. For complex systems, such finiteness cannot be expected. To express and prove properties of these systems, we need a formal language and reasoners that can deal with universal quantification, arithmetic expressions and unbounded data structures at the same time. Thus, in recent years there has been new interest in the handling of firstorder formulas modulo a given background theory. The problem is known to be undecidable in general, and research focuses mostly on methods that solve many problem instances quickly, but sacrifice completeness. We take a different approach and focus on instances of this problem that we can show to be decidable. In this way we can solve the resulting problems efficiently and guarantee termination. This work is based on research by Sofronie-Stokkermans on local theory extensions and on work by Ganzinger and Korovin on instantiation-based firstorder theorem proving. We extend the existing work on local theory extensions, giving new examples of axioms which satisfy a locality condition and using ideas from instantiation-based first-order theorem proving to make local reasoning more efficient. Furthermore, we show that local theory extensions allow us to decide certain verification problems for parameterized systems and develop increasingly complex system models of an automatic train controller on which we demonstrate how to use local reasoning to verify safety properties of such systems.