In the representation approach (TTE) to Computable Analysis those representations of an algebraic or topological structure are of interest, for which the basic predicates and functions become computable. There
Of particular importance is the fact that these include all polynomial time computable functions and predicates. A function or predicate is said to be polynomial time computable provided there exists a Turing machine M and a polynomial p(n), such that M computes the function or recognizes the ...
it is almost equally easy to define and investigate computable functions of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbers for explicit trea...
variable,computablepredicates,andsoforth.Thefundamentalproblemsinvolved are,however,thesameineachcase,andIhavechosenthecomputablenumbersfor explicittreatmentasinvolvingtheleastcumbroustechnique.Ihopeshortlytogive anaccountoftherelationsofthecomputablenumbers,functions,andsoforthto oneanother.Thiswillincludeadevelopmentof...
it is almost equally easy to define and investigate computable functionsof an integral variable or a real or computable variable, computablepredicates, and so forth. The fundamental problems involved are, however, the same in each case, and I have chosen the computable numbersfor explicit treatmen...
investigate computable functions of an integral variable or a real or computablevariable, computable predicates, and so forth. The fundamental problems involvedare, however, the same in each case, and I have chosen the computable numbers forexplicit treatment as involving the least cumbrous technique....
In this paper we prove the Uniformity Principle for Σ–definability over the real numbers extended by open predicates. Using this principle we show that if we have a Σ K -formula, i.e. a formula with quantifier alternations where universal quantifiers are bounded by computabl...
LCF consists of a logic for cpo's and continuous functions, and of a corresponding calculus allowing in particular the formal verification of programs. It differs from the Hoare logic and calculus in the following points. First, the Hoare calculus was developed for a particular programming ...
Although the subject of this paper is ostensibly the computable it is almost equally easy to define and investigate computable functions of an integral variable or a real or computable variable, computable predicates, and so forth. The fundamental problems involved are, however, the same in each ...
computablepredicates,andsoforth.Thefundamentalproblemsinvolvedare,however, thesameineachcase,andIhavechosenthecomputablenumbersforexplicittreatment asinvolvingtheleastcumbroustechnique.Ihopeshortlytogiveanaccountofthe relationsofthecomputablenumbers,functions,andsoforthtooneanother.Thiswill ...