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Ramified recurrence over free algebras has been used over the last two decades to provide machine-independent characterizations of major complexity classes. We consider here ramification for the dual setting, referring to coinductive data and corecurrence rather than inductive data and recurrence. Whereas ramified recurrence is related basically to feasible… (More)

In a previous work, Hofmann and Schöpp have introduced the programming language PURPLE to formalise the common intuition of LOGSPACE-algorithms as pure pointer programs that take as input some structured data (e.g. a graph) and store in memory only a constant number of pointers to the input (e.g. to the graph nodes). It was shown that PURPLE is strictly… (More)

Proof theoretic characterizations of complexity classes are of considerable interest because they link levels of conceptual abstraction to computational complexity. We consider here the provability of functions over coinductive data in a highly expressive, yet proof-theoretically weak, variant of second order logic L + * , which we believe captures the… (More)

—Computational criminology as such is an emerging inter-disciplinary field that applies computer science and mathematical methods to the study of criminological problems. The paper discuss the solutions with these multidisciplinary aspects of criminology, geography, mathematics and computer sciences. In order to understand its nature one has to comprehend… (More)

- Daniel Leivant, Ramyaa
- DICE
- 2011

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… (More)

The vast power of iterated recurrence is tamed by data ramification: if a function over words is definable by ramified recurrence and composition, then it is feasible, i.e. computable in polynomial time, i.e. any computation using the first n input symbols can have at most p(n) distinct configurations, for some polynomial p. Here we prove a dual result for… (More)

A central method for analyzing the asymptotic complexity of a functional program is to extract and then solve a recurrence that expresses evaluation cost in terms of input size. The relevant notion of input size is often specific to a datatype, with measures including the length of a list, the maximum element in a list, and the height of a tree. In this… (More)

The Immerman-Szelepcsenyi Theorem uses an algorithm for cost -connectivity based on inductive counting to prove that NLOGSPACE is closed under complementation. We want to investigate whether counting is necessary for this theorem to hold. Concretely, we show that Nondeterministic Jumping Graph Autmata (ND-JAGs) (pebble automata on graphs), on several… (More)

AIM
The aim was to analyze general incidence, age incidence, laterality, common mode of presentation, staging of the tumor, radiological evidence, histopathological confirmation, management and follow-up of cases, which were diagnosed as retinoblastoma.
DESIGN
Interventional case series study from April 1997 to March 2000.
MATERIALS AND METHODS
Detailed… (More)

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