Partial Derivatives Sample Clauses

Partial Derivatives. T ∈ T In this section we develop the theory of SKA and set up the necessary machinery for Sect. 6 and the completeness proof in Sect. 7. We start by presenting partial derivatives, which provide a termination and continuation map on SF1 . These derivatives allow us to turn the set of synchronous regular terms into a non- deterministic automaton structure, such that the language accepted by e SF1 as a state in this automaton is the same as the semantics of e. Furthermore, partial derivatives turn out to provide a way to algebraically characterise a term by means of acceptance and reachable terms, which is useful in the completeness proof of SF1. The termination and continuation map for SF1-expressions presented below are a trivial extension of the ones from [7]. Intuitively, the termination map is 1 if an expression can immediately terminate, and 0 otherwise; the continuation map of a term w.r.t. A gives us the set of terms reachable with an A-step. ∈ T →
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