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An operational calculus model with the (m,n) - symmetric difference

Wysocki Hubert

Scientific Journal of Polish Naval Academy

2020

R. 61 nr 4 (223)

67--82

The paper determines a non-classical Bittner operational calculus model, in which the derivative is understood as an -symmetric difference . By considering an operation , the formulated model has been generalized.

W pracy określono model dyskretny nieklasycznego rachunku operatorów Bittnera, w którym pochodna rozumiana jest jako różnica -symetryczna . Dokonano uogólnienia opracowanego modelu rozważając operację .

Language Equations with Symmetric Difference

Okhotin A.

Fundamenta Informaticae

2012

Vol. 116, nr 1-4

205-222

The paper investigates the expressive power of language equations with the operations of concatenation and symmetric difference. For equations over every finite alphabet Σ with |Σ| ≥1, it is demonstrated that the sets representable by unique solutions of such equations are exactly the recursive sets over , and the sets representable by their least (greatest) solutions are exactly the recursively enumerable sets (their complements, respectively). If |Σ| ≥ 2, the same characterization holds already for equations using symmetric difference and linear concatenation with regular constants. In both cases, the solution existence problem is Π (0,1)-complete, the existence of a unique, a least or a greatest solution is Π(0,2)-complete, while the existence of finitely many solutions is Σ(0,3)-complete.