58 research outputs found
Multiply-Recursive Upper Bounds with Higman's Lemma
We develop a new analysis for the length of controlled bad sequences in
well-quasi-orderings based on Higman's Lemma. This leads to tight
multiply-recursive upper bounds that readily apply to several verification
algorithms for well-structured systems
PCC '06 / 5th International Workshop on Proof, Computation, Complexity, Ilmenau, July 24 - 25, 2006.
A tier-based typed programming language characterizing Feasible Functionals
The class of Basic Feasible Functionals BFF is the type-2 counterpart of
the class FP of type-1 functions computable in polynomial time. Several
characterizations have been suggested in the literature, but none of these
present a programming language with a type system guaranteeing this complexity
bound. We give a characterization of BFF based on an imperative language
with oracle calls using a tier-based type system whose inference is decidable.
Such a characterization should make it possible to link higher-order complexity
with programming theory. The low complexity (cubic in the size of the program)
of the type inference algorithm contrasts with the intractability of the
aforementioned methods and does not overly constrain the expressive power of
the language
The independence of control structures in abstract programming systems
AbstractAn instance of a control structure is a mapping which takes one or more programs into a new program whose behavior is based on that of the original programs. An instance of a control structure is effective iff it is effectively computable. In order to study the interrelationships of control structures, . we consider abstract programming systems (numberings of the partial recursive functions) in which some control structures, effective or otherwise, are present, but others are not. This paper uses the techniques of recursive function theory, including recursion theorems and priority arguments to prove the independence of certain control structures in abstract programming systems. For example, we have obtained the following results. In effective numberings of the partial recursive functions, the one-one effective Kleene recursion theorem and the one-one effective (partial) if-then-else control structure are independent, but together, they yield all effective control structures. In any effective numbering, the effective Kleene form of the double recursion theorem yields all effective control structures
Quantitative Expressiveness of Instruction Sequence Classes for Computation on Single Bit Registers
The number of instructions of an instruction sequence is taken for its
logical SLOC, and is abbreviated with LLOC. A notion of quantitative
expressiveness is based on LLOC and in the special case of operation over a
family of single bit registers a collection of elementary properties are
established. A dedicated notion of interface is developed and is used for
stating relevant properties of classes of instruction sequence
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