4,169 research outputs found
Implicit complexity for coinductive data: a characterization of corecurrence
We propose a framework for reasoning about programs that manipulate
coinductive data as well as inductive data. Our approach is based on using
equational programs, which support a seamless combination of computation and
reasoning, and using productivity (fairness) as the fundamental assertion,
rather than bi-simulation. The latter is expressible in terms of the former. As
an application to this framework, we give an implicit characterization of
corecurrence: a function is definable using corecurrence iff its productivity
is provable using coinduction for formulas in which data-predicates do not
occur negatively. This is an analog, albeit in weaker form, of a
characterization of recurrence (i.e. primitive recursion) in [Leivant, Unipolar
induction, TCS 318, 2004].Comment: In Proceedings DICE 2011, arXiv:1201.034
Computability and analysis: the legacy of Alan Turing
We discuss the legacy of Alan Turing and his impact on computability and
analysis.Comment: 49 page
KBGIS-2: A knowledge-based geographic information system
The architecture and working of a recently implemented knowledge-based geographic information system (KBGIS-2) that was designed to satisfy several general criteria for the geographic information system are described. The system has four major functions that include query-answering, learning, and editing. The main query finds constrained locations for spatial objects that are describable in a predicate-calculus based spatial objects language. The main search procedures include a family of constraint-satisfaction procedures that use a spatial object knowledge base to search efficiently for complex spatial objects in large, multilayered spatial data bases. These data bases are represented in quadtree form. The search strategy is designed to reduce the computational cost of search in the average case. The learning capabilities of the system include the addition of new locations of complex spatial objects to the knowledge base as queries are answered, and the ability to learn inductively definitions of new spatial objects from examples. The new definitions are added to the knowledge base by the system. The system is currently performing all its designated tasks successfully, although currently implemented on inadequate hardware. Future reports will detail the performance characteristics of the system, and various new extensions are planned in order to enhance the power of KBGIS-2
On tiered small jump operators
Predicative analysis of recursion schema is a method to characterize
complexity classes like the class FPTIME of polynomial time computable
functions. This analysis comes from the works of Bellantoni and Cook, and
Leivant by data tiering. Here, we refine predicative analysis by using a
ramified Ackermann's construction of a non-primitive recursive function. We
obtain a hierarchy of functions which characterizes exactly functions, which
are computed in O(n^k) time over register machine model of computation. For
this, we introduce a strict ramification principle. Then, we show how to
diagonalize in order to obtain an exponential function and to jump outside
deterministic polynomial time. Lastly, we suggest a dependent typed
lambda-calculus to represent this construction
Remote Sensing Information Sciences Research Group, Santa Barbara Information Sciences Research Group, year 3
Research continues to focus on improving the type, quantity, and quality of information which can be derived from remotely sensed data. The focus is on remote sensing and application for the Earth Observing System (Eos) and Space Station, including associated polar and co-orbiting platforms. The remote sensing research activities are being expanded, integrated, and extended into the areas of global science, georeferenced information systems, machine assissted information extraction from image data, and artificial intelligence. The accomplishments in these areas are examined
Some new results on decidability for elementary algebra and geometry
We carry out a systematic study of decidability for theories of (a) real
vector spaces, inner product spaces, and Hilbert spaces and (b) normed spaces,
Banach spaces and metric spaces, all formalised using a 2-sorted first-order
language. The theories for list (a) turn out to be decidable while the theories
for list (b) are not even arithmetical: the theory of 2-dimensional Banach
spaces, for example, has the same many-one degree as the set of truths of
second-order arithmetic.
We find that the purely universal and purely existential fragments of the
theory of normed spaces are decidable, as is the AE fragment of the theory of
metric spaces. These results are sharp of their type: reductions of Hilbert's
10th problem show that the EA fragments for metric and normed spaces and the AE
fragment for normed spaces are all undecidable.Comment: 79 pages, 9 figures. v2: Numerous minor improvements; neater proofs
of Theorems 8 and 29; v3: fixed subscripts in proof of Lemma 3
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