12 research outputs found
Revisiting the Equivalence Problem for Finite Multitape Automata
The decidability of determining equivalence of deterministic multitape
automata (or transducers) was a longstanding open problem until it was resolved
by Harju and Karhum\"{a}ki in the early 1990s. Their proof of decidability
yields a co_NP upper bound, but apparently not much more is known about the
complexity of the problem. In this paper we give an alternative proof of
decidability, which follows the basic strategy of Harju and Karhumaki but
replaces their use of group theory with results on matrix algebras. From our
proof we obtain a simple randomised algorithm for deciding language equivalence
of deterministic multitape automata and, more generally, multiplicity
equivalence of nondeterministic multitape automata. The algorithm involves only
matrix exponentiation and runs in polynomial time for each fixed number of
tapes. If the two input automata are inequivalent then the algorithm outputs a
word on which they differ
The Seven-sphere and its Kac-Moody Algebra
We investigate the seven-sphere as a group-like manifold and its extension to
a Kac-Moody-like algebra. Covariance properties and tensorial composition of
spinors under are defined. The relation to Malcev algebras is
established. The consequences for octonionic projective spaces are examined.
Current algebras are formulated and their anomalies are derived, and shown to
be unique (even regarding numerical coefficients) up to redefinitions of the
currents. Nilpotency of the BRST operator is consistent with one particular
expression in the class of (field-dependent) anomalies. A Sugawara construction
is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files
appende
Existential interpretation. II
A method of existential interpretation was introduced in [2]. It allows proving undecidability of modest strata of many first order theories. Here we improve the method and its presentation, strengthen somewhat the previous results and prove a couple of new results. The reader is not supposed to be acquainted with [2].Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46063/1/153_2005_Article_BF02297651.pd