Violation Semirings in Optimality Theory
 Jason Riggle
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This paper provides a brief algebraic characterization of constraint violations in Optimality Theory (OT). I show that if violations are taken to be multisets over a fixed basis set Con then the merge operator on multisets and a ‘min’ operation expressed in terms of harmonic inequality provide a semiring over violation profiles. This semiring allows standard optimization algorithms to be used for OT grammars with weighted finitestate constraints in which the weights are violationmultisets. Most usefully, because multisets are unordered, the merge operation is commutative and thus it is possible to give a single graph representation of the entire class of grammars (i.e. rankings) for a given constraint set. This allows a neat factorization of the optimization problem that isolates the main source of complexity into a single constant γ denoting the size of the graph representation of the whole constraint set. I show that the computational cost of optimization is linear in the length of the underlying form with the multiplicative constant γ. This perspective thus makes it straightforward to evaluate the complexity of optimization for different constraint sets.
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 Title
 Violation Semirings in Optimality Theory
 Journal

Research on Language and Computation
Volume 7, Issue 1 , pp 112
 Cover Date
 20090301
 DOI
 10.1007/s1116800990630
 Print ISSN
 15707075
 Online ISSN
 15728706
 Publisher
 Springer Netherlands
 Additional Links
 Topics
 Keywords

 Optimality Theory
 Complexity
 Phonology
 Authors

 Jason Riggle ^{(1)}
 Author Affiliations

 1. University of Chicago, Chicago, USA