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We formalise results from computability theory in the theorem prover Isabelle/HOL. Following the textbook by Boolos et al, we formalise Turing machines and relate them to abacus machines and recursive functions. We " tie the knot " between these three computational models by formalising a universal function and obtaining from it a universal Turing machine(More)
The correctness of a routing protocol can be divided into two parts, a liveness property proof and a safety property proof. The former requires that route(s) should be discovered and data be transmitted successfully, while the latter requires that the discovered routes have some desired characters such as containing only benign nodes. While safety(More)
There are numerous textbooks on regular languages. Nearly all of them introduce the subject by describing finite automata and only mentioning on the side a connection with regular expressions. Unfortunately, automata are difficult to formalise in HOL-based theorem provers. The reason is that they need to be represented as graphs, matrices or functions, none(More)