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 ...
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 ...
computable atomic measure μ with the property that the initial segment complexity of each μ-random sequence dominates no computable function, and a computable atomic measure ν with the property that the initial segment complexity of each ν-random sequence is dominated by all computable functions....
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...
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....
computablepredicates,andsoforth.Thefundamentalproblemsinvolvedare,however, thesameineachcase,andIhavechosenthecomputablenumbersforexplicittreatment asinvolvingtheleastcumbroustechnique.Ihopeshortlytogiveanaccountofthe relationsofthecomputablenumbers,functions,andsoforthtooneanother.Thiswill ...
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...
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 ...
variable,computablepredicates,andsoforth.Thefundamentalproblemsinvolved are,however,thesameineachcase,andIhavechosenthecomputablenumbersfor explicittreatmentasinvolvingtheleastcumbroustechnique.Ihopeshortlytogive anaccountoftherelationsofthecomputablenumbers,functions,andsoforthto ...