 # Formal Verification Methods

Osman Hasan, Sofiène Tahar
DOI: 10.4018/978-1-4666-5888-2.ch705
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## Introduction

In order to raise the reliability of system analysis, a system analysis technique is required that can have the precision of paper-and-pencil based mathematical proofs, and thus does not rely upon computer-arithmetic, and utilizes the computers for bookkeeping, to be able to handle complex systems without having to worry about human-errors. Formal verification methods, which are primarily based on theoretical computer science fundamentals like logic calculi, automata theory and strongly type systems, fulfill these requirements. The main principle behind formal analysis of a system is to construct a computer based mathematical model of the given system and formally verify, within a computer, that this model meets rigorous specifications of intended behavior. Due to the mathematical nature of the analysis, 100% accuracy can be guaranteed.

## Key Terms in this Chapter

Higher-Order Logic: A system of deduction with a precise semantics. It differs from the more commonly-known predicate and first-order logics by allowing quantification over function variables. This extension substantially increases the expressiveness of the logic and thus higher-order logic can be used for the formal specification of most mathematical concepts and theories.

Binary Decision Diagram (BDD): A representation of a Boolean expression using a rooted directed acyclic graph (DAG) that consists of terminal (with constant values 0 or 1) or non-terminal nodes (variables). A Reduced ordered BDD (ROBDD), which is a widely used data structure in formal verification, is a BDD with a particular variable order where identical nodes are shared and redundant tests are eliminated.

Tautology: A logical formula is termed to be a tautology (valid) if and only if it is true for all the possible values of its variables. In other words, a formula is a tautology if its negation (¬F) is unsatisfiable. This relationship between satisfiablity and tautology is one of the foundational principles of using SAT solving for equivalence checking.

Temporal Logic: Temporal logic allows us to formally represent time-dependent propositions. For example, propositions like an event would happen in the next time step or sometime in the future or would never happen in the future, can be expressed using temporal logic operators. Temporal logic is used in model-checking to express the properties of interest about the reactive systems.

Formal Verification Methods: Mathematical techniques, often supported by computer-based tools, for the specification and verification of software and hardware systems. The main principle behind formal analysis of a system is to construct a computer based mathematical model of the given system and formally verify, within a computer, that this model meets rigorous specifications of intended behavior.

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