Traditionally, formal languages are defined as sets of words. More recently, the alternative coalgebraic or coinductive representation as infinite tries, i.e., prefix trees branching over the alphabet, has been used to obtain compact and elegant proofs of classic results in language theory. In this article, we study this representation in the Isabelle proof assistant. We define regular operatio...

We show how safety analysis can guide the formal development of controlling software of a safety-critical system. The system is specified in action system framework. The framework is based on a firm mathematical foundation within which the reasoning about the correctness and behavior of the system under development is carried out. We encode information about the identified hazards and their lev...

As a technology ML is oblivious to societal good or bad, and thus, the field of fair machine learning has stepped up propose multiple mathematical definitions, algorithms, systems ensure different notions fairness in applications. Given multitude propositions, it become imperative formally verify metrics satisfied by algorithms on datasets. In this paper, we stochastic satisfiability (SSAT) fra...