In the paper it is investigated, under which conditions a time variable state transformation can be used to change a periodic autonomous system realization into a form with constant real coefficients. Conditions for the transformation to be periodic are further considered, and it is shown that the necessary and sufficient condition to meet the conditions is in that two specific matrices must be...

This paper proposes an expansion of set of primitive constraints available within the Primitive Optimality Theory framework (Eisner, 1997a). This expansion consists of the addition of a new family of constraints—existential implicational constraints, which allow the specification of faithfulness constraints that can be satisfied at a distance—and the definition of two ways to combine simple con...

Morse theory is a fundamental tool for investigating the topology of smooth manifolds. This tool has been extended to discrete structures by Forman, which allows combinatorial analysis and direct computation. This theory relies on discrete gradient vector fields, whose critical elements describe the topology of the structure. The purpose of this work is to construct optimal discrete gradient ve...

Morse theory is a fundamental tool for investigating the topology of smooth manifolds. This tool has been extended to discrete structures by Forman, which allows combinatorial analysis and direct computation. This theory relies on discrete gradient vector fields, whose critical elements describe the topology of the structure. The purpose of this work is to construct optimal discrete gradient ve...

Jackendoff and Lerdahl (1980) point out the resemblance between the ways both linguists and musicologists structure their research objects. This insight gave rise to the proposal of a formal generative theory of tonal music (Lerdahl and Jackendoff 1983), in which they describe musical intuition. Above all, insights from non-linear phonology (cf. Liberman 1975; Liberman and Prince 1977 among oth...

Optimality Theory (OT) has had a lot of attention from the linguistics research community but also still largely lacks cognitive grounding. We used the ACT-R cognitive architecture to gain greater insight into the cognitive grounding issues that OT needs to address, most notably the GEN process and the learning of the constraint ranking. A generic ACT-R 5.0 model was developed guided by OT prin...

A central claim of Optimality Theory is that grammars may differ only in how conflicts among universal well-formedness constraints are resolved: a grammar is precisely a means of resolving such conflicts via a strict priority ranking of constraints. It is shown here how this theory of Universal Grammar yields a highly general Constraint Demotion principle for grammar learning. The resulting lea...

This version differs slightly from the published text due to rewordings introduced in copyediting.

An idempotent phonological grammar maps phonotactically licit forms faithfully to themselves. This paper establishes tight sufficient conditions for idempotency in (classical) Optimality Theory. Building on Tesar (2013), these conditions are derived in two steps. First, idempotency is shown to follow from a general formal condition on the faithfulness constraints. Second, this condition is show...