Abstract: The problems associated with the construction of polynomial complexity computer programs require new techniques and approaches from mathematicians. One of such approaches is representing some class of polynomial algorithms as a certain class of special logical programs. Goncharov and Sviridenko described a logical programming language L0, where programs inductively are obtained from the set of ∆0-formulas using special terms. In their work, a new idea has been proposed to look at the term as a program. The computational complexity of such programs is polynomial. In the same years, a number of other logical languages with similar properties were created. However, the following question remained: can all polynomial algorithms be described in these languages? It is a long-standing problem, and the method of describing some polynomial algorithm in a not Turing complete logical programming language was not previously clear. In this paper, special types of terms and formulas have been found and added to solve this problem. One of the main contributions is the construction of p-iterative terms that simulate the work of the Turing machine. Using p-iterative terms, the work showed that class P is equal to class L, which extends the programming language L0 with p-iterative terms. Thus, it is shown that L is quite expressive and has no halting problem, which occurs in high-level programming languages. For these reasons, the logical language L can be used to create fast and reliable programs. The main limitation of the language L is that the implementation of algorithms of complexity is not higher than polynomial.

Cite: Goncharov S. , Nechesov A.
Solution of the Problem P = L
Mathematics. 2022. V.10. N1. 113 . DOI: 10.3390/math10010113 WOS Scopus РИНЦ OpenAlex

Identifiers:

Web of science:	WOS:000742493500001
Scopus:	2-s2.0-85122104759
Elibrary:	47548331
OpenAlex:	W4206501157

Citing:

DB	Citing
Scopus	11
Web of science	6
OpenAlex	8
Elibrary	11

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