181,662 research outputs found
On ground word problem of term equation systems
We give semi-decision procedures for the ground word problem of variable preserving term equation systems and term equation systems. They are natural improvements of two well known trivial semi-decision procedures. We show the correctness of our procedures
Context unification is in PSPACE
Contexts are terms with one `hole', i.e. a place in which we can substitute
an argument. In context unification we are given an equation over terms with
variables representing contexts and ask about the satisfiability of this
equation. Context unification is a natural subvariant of second-order
unification, which is undecidable, and a generalization of word equations,
which are decidable, at the same time. It is the unique problem between those
two whose decidability is uncertain (for already almost two decades). In this
paper we show that the context unification is in PSPACE. The result holds under
a (usual) assumption that the first-order signature is finite.
This result is obtained by an extension of the recompression technique,
recently developed by the author and used in particular to obtain a new PSPACE
algorithm for satisfiability of word equations, to context unification. The
recompression is based on performing simple compression rules (replacing pairs
of neighbouring function symbols), which are (conceptually) applied on the
solution of the context equation and modifying the equation in a way so that
such compression steps can be in fact performed directly on the equation,
without the knowledge of the actual solution.Comment: 27 pages, submitted, small notation changes and small improvements
over the previous tex
Computations in Large N Matrix Mechanics
The algebraic formulation of Large N matrix mechanics recently developed by
Halpern and Schwartz leads to a practical method of numerical computation for
both action and Hamiltonian problems. The new technique posits a boundary
condition on the planar connected parts X_w, namely that they should decrease
rapidly with increasing order. This leads to algebraic/variational schemes of
computation which show remarkably rapid convergence in numerical tests on some
many- matrix models. The method allows the calculation of all moments of the
ground state, in a sequence of approximations, and excited states can be
determined as well. There are two unexpected findings: a large d expansion and
a new selection rule for certain types of interaction.Comment: 27 page
Canonized Rewriting and Ground AC Completion Modulo Shostak Theories : Design and Implementation
AC-completion efficiently handles equality modulo associative and commutative
function symbols. When the input is ground, the procedure terminates and
provides a decision algorithm for the word problem. In this paper, we present a
modular extension of ground AC-completion for deciding formulas in the
combination of the theory of equality with user-defined AC symbols,
uninterpreted symbols and an arbitrary signature disjoint Shostak theory X. Our
algorithm, called AC(X), is obtained by augmenting in a modular way ground
AC-completion with the canonizer and solver present for the theory X. This
integration rests on canonized rewriting, a new relation reminiscent to
normalized rewriting, which integrates canonizers in rewriting steps. AC(X) is
proved sound, complete and terminating, and is implemented to extend the core
of the Alt-Ergo theorem prover.Comment: 30 pages, full version of the paper TACAS'11 paper "Canonized
Rewriting and Ground AC-Completion Modulo Shostak Theories" accepted for
publication by LMCS (Logical Methods in Computer Science
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