47,671 research outputs found
Tree-Automatic Well-Founded Trees
We investigate tree-automatic well-founded trees. Using Delhomme's
decomposition technique for tree-automatic structures, we show that the
(ordinal) rank of a tree-automatic well-founded tree is strictly below
omega^omega. Moreover, we make a step towards proving that the ranks of
tree-automatic well-founded partial orders are bounded by omega^omega^omega: we
prove this bound for what we call upwards linear partial orders. As an
application of our result, we show that the isomorphism problem for
tree-automatic well-founded trees is complete for level Delta^0_{omega^omega}
of the hyperarithmetical hierarchy with respect to Turing-reductions.Comment: Will appear in Logical Methods of Computer Scienc
The isomorphism problem for tree-automatic ordinals with addition
This paper studies tree-automatic ordinals (or equivalently, well-founded
linearly ordered sets) together with the ordinal addition operation +.
Informally, these are ordinals such that their elements are coded by finite
trees for which the linear order relation of the ordinal and the ordinal
addition operation can be determined by tree automata. We describe an algorithm
that, given two tree-automatic ordinals with the ordinal addition operation,
decides if the ordinals are isomorphic
Model Theoretic Complexity of Automatic Structures
We study the complexity of automatic structures via well-established concepts
from both logic and model theory, including ordinal heights (of well-founded
relations), Scott ranks of structures, and Cantor-Bendixson ranks (of trees).
We prove the following results: 1) The ordinal height of any automatic well-
founded partial order is bounded by \omega^\omega ; 2) The ordinal heights of
automatic well-founded relations are unbounded below the first non-computable
ordinal; 3) For any computable ordinal there is an automatic structure of Scott
rank at least that ordinal. Moreover, there are automatic structures of Scott
rank the first non-computable ordinal and its successor; 4) For any computable
ordinal, there is an automatic successor tree of Cantor-Bendixson rank that
ordinal.Comment: 23 pages. Extended abstract appeared in Proceedings of TAMC '08, LNCS
4978 pp 514-52
Automated verification of shape, size and bag properties.
In recent years, separation logic has emerged as a contender for formal reasoning of heap-manipulating imperative programs. Recent works have focused on specialised provers that are mostly based on fixed sets of predicates. To improve expressivity, we have proposed a prover that can automatically handle user-defined predicates. These shape predicates allow programmers to describe a wide range of data structures with their associated size properties. In the current work, we shall enhance this prover by providing support for a new type of constraints, namely bag (multi-set) constraints. With this extension, we can capture the reachable nodes (or values) inside a heap predicate as a bag constraint. Consequently, we are able to prove properties about the actual values stored inside a data structure
Homeomorphic Embedding for Online Termination of Symbolic Methods
Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems
COSMICAH 2005: workshop on verification of COncurrent Systems with dynaMIC Allocated Heaps (a Satellite event of ICALP 2005) - Informal Proceedings
Lisboa Portugal, 10 July 200
- …