Implementing Dynamic Programming in Computability Logic Web

• URL: http://arxiv.org/abs/2304.01539v1
• Date: Tue, 4 Apr 2023 05:33:43 GMT
• Title: Implementing Dynamic Programming in Computability Logic Web
• Authors: Keehang Kwon
• Abstract summary: We present a novel definition of an algorithm and its corresponding algorithm language called CoLweb. CoLweb forces us to a high-level, proof-carrying, distributed-style approach to algorithm design for both non-distributed computing and distributed one. We refine Horn clause definitions into two kinds: blind-univerally-quantified (BUQ) ones and parallel-universally-quantified (PUQ) ones.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We present a novel definition of an algorithm and its corresponding algorithm language called CoLweb. The merit of CoLweb [1] is that it makes algorithm design so versatile. That is, it forces us to a high-level, proof-carrying, distributed-style approach to algorithm design for both non-distributed computing and distributed one. We argue that this approach simplifies algorithm design. In addition, it unifies other approaches including recursive logical/functional algorithms, imperative algorithms, object-oriented imperative algorithms, neural-nets, interaction nets, proof-carrying code, etc. As an application, we refine Horn clause definitions into two kinds: blind-univerally-quantified (BUQ) ones and parallel-universally-quantified (PUQ) ones. BUQ definitions corresponds to the traditional ones such as those in Prolog where knowledgebase is $not$ expanding and its proof procedure is based on the backward chaining. On the other hand, in PUQ definitions, knowledgebase is $expanding$ and its proof procedure leads to forward chaining and {\it automatic memoization}.

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