Reducing complexity of tail-biting trellises
Heide Gluesing-Luerssen, G. David Forney, Jr
TL;DR
This paper presents a comprehensive criterion for the local irreducibility of tail-biting trellises, improving understanding of their structural complexity and reduction conditions.
Contribution
It introduces a necessary and sufficient condition for local irreducibility of tail-biting trellises, extending previous partial criteria.
Findings
Local reducibility occurs if trellis is not state-trim, branch-trim, proper, observable, and controllable.
Conditions for local irreducibility are refined using notions of 'almost unobservability/uncontrollability'.
A complete criterion for local irreducibility of tail-biting trellises is provided.
Abstract
It is shown that a trellis realization can be locally reduced if it is not state-trim, branch-trim, proper, observable, and controllable. These conditions are not sufficient for local irreducibility. Making use of notions that amount to "almost unobservability/uncontrollability", a necessary and sufficient criterion of local irreducibility for tail-biting trellises is presented.
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Taxonomy
Topicssemigroups and automata theory · Advanced Algebra and Logic · Logic, programming, and type systems