Computation Engineering, Softcover reprint of hardcover 1st ed. 2006
Applied Automata Theory and Logic

It takes more e?ort to verify that digital system designs are correct than it does to design them, and as systems get more complex the proportion of cost spent on veri?cation is increasing (one estimate is that veri?cation complexity rises as the square of design complexity). Although this veri?cation crisis was predicted decades ago, it is only recently that powerful methods based on mathematical logic and automata theory have come to the designers? rescue. The ?rst such method was equivalence checking, which automates Boolean algebra calculations.Nextcamemodelchecking,whichcanautomatically verify that designs have ? or don?t have ? behaviours of interest speci?ed in temporal logic. Both these methods are available today in tools sold by all the major design automation vendors. It is an amazing fact that ideas like Boolean algebra and modal logic, originating frommathematicians andphilosophersbeforemodern computers were invented, have come to underlie computer aided tools for creating hardware designs. The recent success of ?formal? approaches to hardware veri?cation has lead to the creation of a new methodology: assertion based design, in which formal properties are incorporated into designs and are then validated by a combination of dynamic simulation and static model checking. Two industrial strength property languages based on tem- ral logic are undergoing IEEE standardisation. It is not only hardwaredesignand veri?cation that is changing: new mathematical approaches to software veri?cation are starting to be - ployed. Microsoft provides windows driver developers with veri?cation tools based on symbolic methods.

Mathematical Preliminaries.- Cardinalities and Diagonalization.- Binary Relations.- Mathematical Logic, Induction, Proofs.- Dealing with Recursion.- Strings and Languages.- Machines, Languages, DFA.- NFA and Regular Expressions.- Operations on Regular Machinery.- The Automaton/Logic Connection, Symbolic Techniques.- The ‘Pumping’ Lemma.- Context-free Languages.- Push-down Automata and Context-free Grammars.- Turing Machines.- Basic Undecidability Proofs.- Advanced Undecidability Proofs.- Basic Notions in Logic including SAT.- Complexity Theory and NP-Completeness.- DFA for Presburger Arithmetic.- Model Checking: Basics.- Model Checking: Temporal Logics.- Model Checking: Algorithms.- Conclusions.

Approaches automata theory and logic as the underlying engineering mathematics for Computation Engineering Covers classical topics such as the Rice's Theorem, as well as modern topics such as Model checking, Buchi Automata, and temporal Logic Restores the Automaton-Logic connection missing in most undergraduate books on automata theory Employs many interactive tools to illustrate key concepts Includes supplementary material: sn.pub/extras