Decidability of the Equational Theory of the Continuous Geometry $CG(\Bbb {F})$

Decidability and Tameness in the Theory of Finite Semigroups

Countable composition closedness and integer-valued continuous functions in pointfree topology

‎For any archimedean$f$-ring $A$ with unit in whichbreak$awedge‎ ‎(1-a)leq 0$ for all $ain A$‎, ‎the following are shown to be‎ ‎equivalent‎: ‎ ‎1‎. ‎$A$ is isomorphic to the $l$-ring ${mathfrak Z}L$ of all‎ ‎integer-valued continuous functions on some frame $L$‎. 2‎. ‎$A$ is a homomorphic image of the $l$-ring $C_{Bbb Z}(X)$‎ ‎of all integer-valued continuous functions‎, ‎in the usual se...

Combining Equational Tree Automata over AC and ACI Theories

In this paper, we study combining equational tree automata in two different senses: (1) whether decidability results about equational tree automata over disjoint theories E1 and E2 imply similar decidability results in the combined theory E1 ∪ E2; (2) checking emptiness of a language obtained from the Boolean combination of regular equational tree languages. We present a negative result for the...

Instrument dependency of Kubelka-Munk theory in computer color matching

Different industries are usually faced with computer color matching as an important problem. The most famous formula which is commonly used for recipe prediction is based on Kubelka-Munk K-M theory. Considering that spectrophotometer’s geometry and its situation influence the measured spectral values, the performance of this method can be affected by the instrument. In the present study, three ...

Decidability of the equational theory of allegories

Freyd and Scedrov showed that the equational theory of representable allegories (essentially those allegories which have a settheoretic representation as relations) is decidable. This paper proves that the pure equational theory of allegories is decidable.