41,861 research outputs found
Self-Specifying Machines
We study the computational power of machines that specify their own
acceptance types, and show that they accept exactly the languages that
\manyonesharp-reduce to NP sets. A natural variant accepts exactly the
languages that \manyonesharp-reduce to P sets. We show that these two classes
coincide if and only if \psone = \psnnoplusbigohone, where the latter class
denotes the sets acceptable via at most one question to \sharpp followed by
at most a constant number of questions to \np.Comment: 15 pages, to appear in IJFC
Naturally Embedded Query Languages
We investigate the properties of a simple programming language whose main computational engine is structural recursion on sets. We describe a progression of sublanguages in this paradigm that (1) have increasing expressive power, and (2) illustrate robust conceptual restrictions thus exhibiting interesting additional properties. These properties suggest that we consider our sublanguages as candidates for "query languages". Viewing query languages as restrictions of our more general programming language has several advantages. First, there is no "impedance mismatch" problem; the query languages are already there, so they share common semantic foundation with the general language. Second, we suggest a uniform characterization of nested relational and complex-object algebras in terms of some surprisingly simple operators; and we can make comparisons of expressiveness in a general framework. Third, we exhibit differences in expressive power that are not always based on complexity arguments..
Combining Relational Algebra, SQL, Constraint Modelling, and Local Search
The goal of this paper is to provide a strong integration between constraint
modelling and relational DBMSs. To this end we propose extensions of standard
query languages such as relational algebra and SQL, by adding constraint
modelling capabilities to them. In particular, we propose non-deterministic
extensions of both languages, which are specially suited for combinatorial
problems. Non-determinism is introduced by means of a guessing operator, which
declares a set of relations to have an arbitrary extension. This new operator
results in languages with higher expressive power, able to express all problems
in the complexity class NP. Some syntactical restrictions which make data
complexity polynomial are shown. The effectiveness of both extensions is
demonstrated by means of several examples. The current implementation, written
in Java using local search techniques, is described. To appear in Theory and
Practice of Logic Programming (TPLP)Comment: 30 pages, 5 figure
A Theory of Formal Synthesis via Inductive Learning
Formal synthesis is the process of generating a program satisfying a
high-level formal specification. In recent times, effective formal synthesis
methods have been proposed based on the use of inductive learning. We refer to
this class of methods that learn programs from examples as formal inductive
synthesis. In this paper, we present a theoretical framework for formal
inductive synthesis. We discuss how formal inductive synthesis differs from
traditional machine learning. We then describe oracle-guided inductive
synthesis (OGIS), a framework that captures a family of synthesizers that
operate by iteratively querying an oracle. An instance of OGIS that has had
much practical impact is counterexample-guided inductive synthesis (CEGIS). We
present a theoretical characterization of CEGIS for learning any program that
computes a recursive language. In particular, we analyze the relative power of
CEGIS variants where the types of counterexamples generated by the oracle
varies. We also consider the impact of bounded versus unbounded memory
available to the learning algorithm. In the special case where the universe of
candidate programs is finite, we relate the speed of convergence to the notion
of teaching dimension studied in machine learning theory. Altogether, the
results of the paper take a first step towards a theoretical foundation for the
emerging field of formal inductive synthesis
Strengths and Weaknesses of Quantum Computing
Recently a great deal of attention has focused on quantum computation
following a sequence of results suggesting that quantum computers are more
powerful than classical probabilistic computers. Following Shor's result that
factoring and the extraction of discrete logarithms are both solvable in
quantum polynomial time, it is natural to ask whether all of NP can be
efficiently solved in quantum polynomial time. In this paper, we address this
question by proving that relative to an oracle chosen uniformly at random, with
probability 1, the class NP cannot be solved on a quantum Turing machine in
time . We also show that relative to a permutation oracle chosen
uniformly at random, with probability 1, the class cannot be
solved on a quantum Turing machine in time . The former bound is
tight since recent work of Grover shows how to accept the class NP relative to
any oracle on a quantum computer in time .Comment: 18 pages, latex, no figures, to appear in SIAM Journal on Computing
(special issue on quantum computing
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