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In computer science and mathematics, more precisely in automata theory, model theory and formal language, a regular numerical predicate is a kind of relation over integers. Regular numerical predicates can also be considered as a subset of for some arity . One of the main interests of this class of predicates is that it can be defined in plenty of different ways, using different logical formalisms. Furthermore, most of the definitions use only basic notions, and thus allows to relate foundations of various fields of fundamental computer science such as automata theory, syntactic semigroup, model theory and semigroup theory.
The class of regular numerical predicate is denoted ,[1]: 140 [2] and REG.[3]
^Cite error: The named reference Peladeau was invoked but never defined (see the help page).
^Choffrut, Christian (January 2008). "Deciding whether a relation defined in Presburger logic can be defined in weaker logics". RAIRO - Theoretical Informatics and Applications. 42 (1): 121–135. doi:10.1051/ita:2007047.
^Straubing, Howard (1994). Finite Automata, Formal Logic and Circuit Complexity. Birkhäser. ISBN 978-1-4612-0289-9.
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