An algorithm of Beyer and Hedetniemi for generating unlabeled rooted trees is extended to generate unlabeled free trees. Abstract An algorithm of Beyer and Hedetniemi for generating unlabeled rooted trees is extended to generate unlabeled free trees. “The Beyer-Hedetniemi technique is refined to produce only one member of each equivalence class of rooted trees under isomorphism of the underlyin...

For a given numeration system, the successor function maps the representation of an integer n onto the representation of its successor n+1. In a general setting, the successor function maps the n-th word of a genealogically ordered language L onto the (n+1)-th word of L. We show that, if the ratio of the number of elements of length n+ 1 over the number of elements of length n of the language h...

abstract. This paper presents a family of rst order feature tree theories, indexed by the theory of the feature labels used to build the trees. A given feature label theory, which is required to carry an appropriate notion of sets, is conservatively extended to a theory of feature trees with the predicates xt]y (feature t leads from the root of tree x to the tree y, where we require t to be a g...

We give a new successor data structure which improves upon the index size of the Pǎtraşcu-Thorup data structures, reducing the index size from O(nw) bits to O(n logw) bits, with optimal probe complexity. Alternatively, our new data structure can be viewed as matching the space complexity of the (probe-suboptimal) z-fast trie of Belazzougui et al. Thus, we get the best of both approaches with re...

A first-order sentence θ of vocabulary σ ∪ {S} is successor-invariant in the finite if for every finite σ-structure M and successor relations S1 and S2 on M, (M, S1) |= θ ⇐⇒ (M, S2) |= θ. In this paper I give an example of a non-first-order definable class of finite structures which is, however, defined by a successor-invariant first-order sentence. This strengthens a corresponding result for o...

This paper presents a family of rst order feature tree theories, indexed by the theory of the feature labels used to build the trees. A given feature label theory, which is required to carry an appropriate notion of sets, is conservatively extended to a theory of feature trees with the predicates xt]y (feature t leads from the root of tree x to the tree y), where we have to require t to be a gr...

This paper introduces a sequence of λ-expressions modelling the binary expansion of integers. We derive expressions computing the test for zero, the successor function, and the predecessor function, thereby showing the sequence to be an adequate numeral system. These functions can be computed efficiently. Their complexity is independent of the order of evaluation.