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We show that for finite n ≥ 3, every first-order axiomatisation of the varieties of representable n-dimensional cylindric algebras, diagonal-free cylindric algebras , polyadic algebras, and polyadic equality algebras contains an infinite number of non-canonical formulas. We also show that the class of structures for each of these varieties is… (More)

We show that for finite n ≥ 3 the class of representable cylindric algebras RCA n cannot be axiomatised by canonical first-order formulas. So, although RCA n is known to be canonical, which means that it is closed under canonical extensions, there is no axioma-tisation where all the formulas are preserved by canonical extensions. In fact, we show that every… (More)

A commonly studied means of parameterizing graph problems is the deletion distance from triviality (Guo et al., Parameterized and exact computation, Springer, Berlin, pp. 162–173, 2004), which counts vertices that need to be deleted from a graph to place it in some class for which efficient algorithms are known. In the context of graph isomorphism, we… (More)

We show that for various classes $$\mathcal {C}$$ C of sparse graphs, and several measures of distance to such classes (such as edit distance and elimination distance), the problem of determining the distance of a given graph G to $$\mathcal {C}$$ C is fixed-parameter tractable. The results are based on two general techniques. The first of these, building… (More)

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