Hardware protocols, aircraft control software, and communication protocols do not terminate. They are verified using ω-automata and LTL. The model checking problem: "Does a finite-state system satisfy a temporal logic formula?" reduces to checking emptiness of the product of a system's automaton and the negation of the formula's Büchi automaton.
: The concept of ω-semigroups (or Wilke algebras ) provides an algebraic foundation for ω-languages, splitting an infinite word into a finite prefix followed by an infinite periodic tail. Download Infinite words automata semigroups logic and games
Algebraic automata theory models finite automata using finite semigroups. The syntactic semigroup of an ω-language is a critical algebraic invariant. The links star-free ω-languages to first-order logic, while Eilenberg’s variety theorem connects pseudovarieties of finite semigroups to varieties of ω-regular languages. : The concept of ω-semigroups (or Wilke algebras
Managing infinite streams of data in real-time environments. 4. Key Resources to Study The links star-free ω-languages to first-order logic, while