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We provide an explicit characterization of the properties of primitive recursive functions that are decidable or semi-decidable, given a primitive recursive index for the function. The result is much more general as it applies to any c.e. class of total computable functions. This is an analog of Rice and Rice-Shapiro theorem, for restricted classes of total computable functions.
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursi
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn formula equ
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursi
This paper proposes a recursive diffeomorphism based regression method for one-dimensional generalized mode decomposition problem that aims at extracting generalized modes $alpha_k(t)s_k(2pi N_kphi_k(t))$ from their superposition $sum_{k=1}^K alpha_k
In this paper we present a cut-free sequent calculus, called SeqS, for some standard conditional logics, namely CK, CK+ID, CK+MP and CK+MP+ID. The calculus uses labels and transition formulas and can be used to prove decidability and space complexity