94,883 research outputs found
Representing a P-complete problem by small trellis automata
A restricted case of the Circuit Value Problem known as the Sequential NOR
Circuit Value Problem was recently used to obtain very succinct examples of
conjunctive grammars, Boolean grammars and language equations representing
P-complete languages (Okhotin, http://dx.doi.org/10.1007/978-3-540-74593-8_23
"A simple P-complete problem and its representations by language equations",
MCU 2007). In this paper, a new encoding of the same problem is proposed, and a
trellis automaton (one-way real-time cellular automaton) with 11 states solving
this problem is constructed
Efficient Solution of Language Equations Using Partitioned Representations
A class of discrete event synthesis problems can be reduced to solving
language equations f . X ⊆ S, where F is the fixed component and S the
specification. Sequential synthesis deals with FSMs when the automata for F and
S are prefix closed, and are naturally represented by multi-level networks with
latches. For this special case, we present an efficient computation, using
partitioned representations, of the most general prefix-closed solution of the
above class of language equations. The transition and the output relations of
the FSMs for F and S in their partitioned form are represented by the sets of
output and next state functions of the corresponding networks. Experimentally,
we show that using partitioned representations is much faster than using
monolithic representations, as well as applicable to larger problem instances.Comment: Submitted on behalf of EDAA (http://www.edaa.com/
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The effect of multiple knowledge sources on learning and teaching
Current paradigms for machine-based learning and teaching tend to perform their task in isolation from a rich context of existing knowledge. In contrast, the research project presented here takes the view that bringing multiple sources of knowledge to bear is of central importance to learning in complex domains. As a consequence teaching must both take advantage of and beware of interactions between new and existing knowledge. The central process which connects learning to its context is reasoning by analogy, a primary concern of this research. In teaching, the connection is provided by the explicit use of a learning model to reason about the choice of teaching actions. In this learning paradigm, new concepts are incrementally refined and integrated into a body of expertise, rather than being evaluated against a static notion of correctness. The domain chosen for this experimentation is that of learning to solve "algebra story problems." A model of acquiring problem solving skills in this domain is described, including: representational structures for background knowledge, a problem solving architecture, learning mechanisms, and the role of analogies in applying existing problem solving abilities to novel problems. Examples of learning are given for representative instances of algebra story problems. After relating our views to the psychological literature, we outline the design of a teaching system. Finally, we insist on the interdependence of learning and teaching and on the synergistic effects of conducting both research efforts in parallel
Set Unification
The unification problem in algebras capable of describing sets has been
tackled, directly or indirectly, by many researchers and it finds important
applications in various research areas--e.g., deductive databases, theorem
proving, static analysis, rapid software prototyping. The various solutions
proposed are spread across a large literature. In this paper we provide a
uniform presentation of unification of sets, formalizing it at the level of set
theory. We address the problem of deciding existence of solutions at an
abstract level. This provides also the ability to classify different types of
set unification problems. Unification algorithms are uniformly proposed to
solve the unification problem in each of such classes.
The algorithms presented are partly drawn from the literature--and properly
revisited and analyzed--and partly novel proposals. In particular, we present a
new goal-driven algorithm for general ACI1 unification and a new simpler
algorithm for general (Ab)(Cl) unification.Comment: 58 pages, 9 figures, 1 table. To appear in Theory and Practice of
Logic Programming (TPLP
Quantum and Classical Integrable Systems
The key concept discussed in these lectures is the relation between the
Hamiltonians of a quantum integrable system and the Casimir elements in the
underlying hidden symmetry algebra. (In typical applications the latter is
either the universal enveloping algebra of an affine Lie algebra, or its
q-deformation.) A similar relation also holds in the classical case. We discuss
different guises of this very important relation and its implication for the
description of the spectrum and the eigenfunctions of the quantum system.
Parallels between the classical and the quantum cases are thoroughly discussed.Comment: 59 pages, LaTeX2.09 with AMS symbols. Lectures at the CIMPA Winter
School on Nonlinear Systems, Pondicherry, January 199
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