this paper we present a type-theoretic approach to this problem. We will develop a fairly natural linear type system which has the property that all definable functions are non-size increasing and which boasts higher-order recursion on datatypes without any predicativity restriction. We will show that nevertheless all definable first-order functions are polynomial time computable even if they contain higher-order functions as subexpressions

This paper concentrates on query unnesting (also known as query decorrelation), an optimization that, even though improves performance considerably, is not treated properly (if at all) by most OODB systems. Our framework generalizes many unnesting techniques proposed recently in the literature and is capable of removing any form of query nesting using a very simple and efficient algorithm. The simplicity of our method is due to the use of the monoid comprehension calculus as an intermediate form for OODB queries. The monoid comprehension calculus treats operations over multiple collection types, aggregates, and quantifiers in a similar way, resulting in a uniform way of unnesting queries, regardless of their type of nesting.

The purpose of this thesis is to give a "foundational" characterization of some common complexity classes. Such a characterization is distinguished by the fact that no explicit resource bounds are used. For example, we characterize the polynomial time computable functions without making any direct reference to polynomials, time, or even computation. Complexity classes characterized in this way include polynomial time, the functional polytime hierarchy, the logspace decidable problems, and NC. After developing these "resource free" definitions, we apply them to redeveloping the feasible logical system of Cook and Urquhart, and show how this first-order system relates to the second-order system of Leivant. The connection is an interesting one since the systems were defined independently and have what appear to be very different rules for the principle of induction. Furthermore it is interesting to see, albeit in a very specific context, how to retract a second order statement, ("inducti...

We develop new methods to statically bound the resources needed for the execution of systems of concurrent, interactive threads.

Abstract not found

We present a higher-order functional notation for polynomial-time computation with an arbitrary 0, 1-valued oracle. This formulation provides a linguistic characterization for classes such as NP and BPP, as well as a notation for probabilistic polynomialtime functions. The language is derived from Hofmann 's adaptation of Bellantoni-Cook safe recursion, extended to oracle computation via work derived from that of Kapron and Cook. Like Hofmann's language, ours is an applied typed lambda calculus with complexity bounds enforced by a type system. The type system uses a modal operator to distinguish between two sorts of numerical expressions. Recursion can take place on only one of these sorts. The proof that the language captures precisely oracle polynomial time is model-theoretic, using adaptations of various techniques from category theory.

This paper develops a query language for sequence databases, such as genome databases and text databases. The language, called SequenceDatalog, extends classical Datalog with interpreted function symbols for manipulating sequences. It has both a clear operational and declarative semantics, based on a new notion called the extended active domain of a database. The extended domain contains all the sequences in the database and all their subsequences. This idea leads to a clear distinction between safe and unsafe recursion over sequences: safe recursion stays inside the extended active domain, while unsafe recursion does not. By carefully limiting the amountof unsafe recursion, the paper develops a safe and expressive subset of Sequence Datalog. As part of the development, a new type of transducer is introduced, called a generalized sequence transducer. Unsafe recursion is allowed only within these generalized transducers. Generalized transducers extend ordinary transducers by allowing them to invoke other transducers as "subroutines." Generalized transducers can be implemented in Sequence Datalog in a straightforward way. Moreover, their introduction into the language leads to simple conditions that guarantee safety and finiteness. This paper develops two such conditions. The first condition expresses exactly the class of ptime sequence functions; and the second expresses exactly the class of elementary sequence functions.

We investigate the expressive power of the typed -calculus when expressing computations over finite structures, i.e., databases. We show that the simply typed -calculus can express various database query languages such as the relational algebra, fixpoint logic, and the complex object algebra. In our embeddings, inputs and outputs are -terms encoding databases, and a program expressing a query is a -term which types when applied to an input and reduces to an output.

In previous work the author has introduced a lambda calculus SLR with modal and linear types which serves as an extension of Bellantoni-Cook's function algebra BC to higher types. It is a step towards a functional programming language in which all programs run in polynomial time. In this paper we develop a semantics of SLR using BCK-algebras consisting of certain polynomial-time algorithms. It will follow from this semantics that safe recursion with arbitrary result type built up from N and ( as well as recursion over trees and other data structures remains within polynomial time. In its original formulation SLR supported only natural numbers and recursion on notation with first order functional result type. 1 Introduction In [10] and [11] we have introduced a lambda calculus SLR which generalises the Bellantoni-Cook characterisation of PTIME [2] to higher-order functions. The separation between normal and safe variables which is crucial to the Bellantoni-Cook system has been achieved...

Compare first-order functional programs with higher-order programs allowing functions as function parameters. Can the the first program class solve fewer problems than the second? The answer is no: both classes are Turing complete, meaning that they can compute all partial recursive functions. In particular, higher-order values may be first-order simulated by use of the list constructor ‘cons’ to build function closures. This paper uses complexity theory to prove some expressivity results about small programming languages that are less than Turing complete. Complexity classes of decision problems are used to characterize the expressive power of functional programming language features. An example: second-order programs are more powerful than first-order, since a function f of type [Bool]-〉Bool is computable by a cons-free first-order functional program if and only if f is in PTIME, whereas f is computable by a cons-free second-order program if and only if f is in EXPTIME. Exact characterizations are given for those problems of type [Bool]-〉Bool solvable by programs with several combinations of operations on data: presence or absence of constructors; the order of data values: 0, 1, or higher; and program control structures: general recursion, tail recursion, primitive recursion.