Equivalence Classes of Boolean Functions

Stanković, Radomir S.; Stanković, Stanislav; Astola, Helena; Astola, Jaakko

doi:10.1007/978-3-031-79812-2_1

Cited by 1 publication

(3 citation statements)

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“…The non-logical symbols are the so-called propositional variables (p, q, r), and the logical symbols are the so-called logical connectors (¬, ∧, ∨,→, ↔), and the punctuation marks are usually parentheses ( ), braces [1], brackets [ ], commas, etc. Then, the rules must be taken into account to join the elements of the vocabulary, this set of rules is called formal grammar or syntax.…”

Section: Temporal Logic Ktmentioning

confidence: 99%

“…This is the case with the theory of automata, which combines ideas from engineering, linguistics, mathematics, philosophy, etc. [1] The theory of automata is a theoretical discipline that belongs to a broader field. Computer science specifies algorithmic processes using a formal language [2].…”

Section: Introductionmentioning

confidence: 99%

“…V. Shestakov (1907Shestakov ( -1987 [13] developed this model in 1934/35 but didn't publish it until 1941. In 1938, in two parts of the world, C. Shannon and Japanese A. Hanzawa [1]. Shannon's theory is today's most popular despite having no relationship with the other.…”

Section: Introductionmentioning

confidence: 99%

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The Influence of Temporal Logic on Finite Automata

Kareem¹,

Senjari²

2023

(AREJ)

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The theory of automata combines ideas from engineering, linguistics, mathematics, philosophy, etc. The Entscheidungsproblem asks if it is possible to design a series of steps that replaces a mathematician. An automaton is an abstract machine that processes data. C. Shannon's theory is today's most popular despite having no relationship with the other. The Kt system is called "minimal" because it makes no assumptions about the structure of time. In LKt, we have four monary temporal operators, F, P, G and H, which are mutually interdefinable. Interdefinability means that we will pass logic in the future is the same as saying I will never fail logic, interpreting not passing logic as failing logic. The minimal system syntax of temporal logic introduces operators that have the property of being defined in terms of others. Modal logic studies the reasoning that involves the use of expressions "necessarily" and "possibly". In this article, we will represent through a finite automaton the temporal logic formula Fp. It allows us to see an acceptance pattern for Fp by considering two variables: p and q. Kt's axiomatic system of time expresses the idea that both the present and the past are fixed, if it has always been in the past that it will be some time in the future that p is now. No philosophical argument supports deterministic time flow; the logic of time must be open.Temporal logic has revived many old problems, from the Megaric-Stoics to the minimal system of temporal logic. Our work suggests that the future operators of system Kt follow an evaluation pattern, but we must be cautious because this pattern can only apply to models whose time flow is based on instants and precedence relations.

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Section: Temporal Logic Ktmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%