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semantic programming and Polynomially Computable Representations

Siberian Advances in Mathematics 2023年第1期33卷 66-85页

作者： Nechesov, A.V. Sobolev Institute of Mathematics Novosibirsk 630090 Russian Federation

Abstract: In the present article, we consider the question on existence of polynomially computablerepresentations for basic syntactic constructions of the first-order logic and for objects of semanticprogramming (such as L-programs andL-formulas). We prove that the sets of linear ortree-like derivations in the first-order predicate calculus admits a polynomially computablerepresentation. We also obtain a series of assertions that allow us to prove polynomialcomputability in a more efficient way. Among them, we mention the generalized PAG-theoremwith polynomially computable initial data and an assertion on p-iterative terms with weakened estimates. Ourresults may be useful for construction of logical programming languages, in smart contracts, aswell as for developing fast algorithms for automatic proof verification. © 2023, Pleiades Publishing, Ltd.

关键词： artificial intelligence Gandy theorem GNF-systems iterative terms PAG-theorem polynomial computability proof theory proof verification semantic programming smart contracts

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Conditional terms in semantic programming

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SIBERIAN MATHEMATICAL JOURNAL 2017年第5期58卷 794-800页

作者： Goncharov, S. S. Novosibirsk State Univ Sobolev Inst Math Novosibirsk Russia

For constructing an enrichment of the language with restricted quantifiers, we extend the construction of conditional terms. We show that the so-obtained extension of the language of formulas with restricted quantifie... 详细信息

关键词： formula term restricted quantifier Delta(0)-formula Sigma-formula semantic programming computability computability over abstract structures conditional term

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Recursive Terms in semantic programming

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SIBERIAN MATHEMATICAL JOURNAL 2018年第6期59卷 1014-1023页

作者： Goncharov, S. S. Sviridenko, D. I. Sobolev Inst Math Novosibirsk Russia

For constructing an enrichment of a language with restricted quantifiers, we extend the notion of term by the construction of the terms conditional and recursive with respect to lists. We show that the so-obtained extension of the language of formulas with restricted quantifiers over structures with hereditary finite lists is a conservative enrichment and the new terms are -definable in the basic language.

关键词： formula term restricted quantifier (0)-formula -formula sigma-formula semantic programming computability computability over abstract structures conditional term recursive term model hereditary finite list hereditary finite set

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Some Questions on Polynomially Computable Representations for Generating Grammars and Backus–Naur Forms

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Siberian Advances in Mathematics 2022年第4期32卷 299-309页

作者： Nechesov, A.V. Sobolev Institute of Mathematics Novosibirsk 630090 Russian Federation

Abstract: In the present article, we consider the question on modeling Backus–Naur forms(BNF-systems) and generating grammars in GNF-systems. GNF-systems serve as the base forconstruction of monotone operators whose least fixed points are polynomially computable. Weobtain our results by construction of GNF-systems and application of a generalized polynomialanalog of Gandy’s fixed point theorem. This allows us to answer some questions on existence ofa polynomially computable representation for the set of derivations in generating ***, we show that, for each GNF-system modeling a BNF-system and every nonterminalsymbol in the BNF-system, the set of preimages in the GNF-system of representations of thissymbol is polynomially computable. This result allows us to encode all definable constructions ofthe BNF-system, including the syntax of programs in high-level programming languages, so thatthey become recognizable in polynomial time. © 2022, Pleiades Publishing, Ltd.

关键词： artificial intelligence Backus–Naur forms blockchain BNF-systems Chomsky grammars Gandy’s theorem generating grammars GNF-systems PAG-theorem polynomial computability programming languages semantic programming smart contracts

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semantics, Logics, and Calculi: Essays Dedicated to Hanne Riis Nielson and Flemming Nielson on the Occasion of Their 60th Birthdays 1

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丛书名： Lecture Notes in Computer Science 9560

2016年

作者： Christian W. Probst, Chris Hankin, René Rydhof Hansen (eds.)

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