A Simple Proof That Optimality Theory Is Computationally Intractable

2006 ◽  
Vol 37 (2) ◽  
pp. 271-275 ◽  
Author(s):  
William J. Idsardi
Keyword(s):  
Simple Proof ◽  
Optimality Theory ◽  
Np Hard ◽  
Rule Based ◽  
Generation Problem

Adapting arguments from Eisner 1997, 2000, this remark provides a simple proof that the generation problem for Optimality Theory (Prince and Smolensky 2004) is NP-hard. The proof needs only the binary evaluation of constraints and uses only constraints generally employed in the Optimality Theory literature. In contrast, rule-based derivational systems are easily computable, belonging to the class of polynomialtime algorithms, P (Eisner 2000).

OPTIMALITY THEORY. René Kager. New York: Cambridge University Press, 1999. Pp. xiii + 452. $64.95 cloth, $24.95 paper.

2001 ◽  
Vol 23 (3) ◽  
pp. 422-423
Author(s):  
Daniel Dinnsen ◽  
Laura W. McGarrity ◽  
Kathleen M. O'Connor
Keyword(s):  
New York ◽  
Optimality Theory ◽  
Rule Based ◽  
Cambridge University ◽  
Basic Understanding

This volume is an excellent introduction to the principles and workings of optimality theory, a relatively new constraint-based framework. The focus is on phonology, which is where the theory thus far has had its greatest impact. A basic understanding of phonology and earlier rule-based derivational theories is assumed. At appropriate points, Kager distinguishes the different claims made by optimality theory and derivational theories. The exercises and suggested readings at the end of each chapter make the book highly suitable as a textbook. The conclusion of each chapter also provides a good summary of the main points. In addition to conventional subject and language indexes, a helpful index of constraints is included with page numbers for where the constraint is defined and used.

scholarly journals Optimaalsusteooria fonoloogias

2013 ◽  
Vol 4 (1) ◽  
pp. 111-126
Author(s):  
Külli Prillop
Keyword(s):  
Optimality Theory ◽  
Explanatory Power ◽  
Phonological Development ◽  
Theoretical Frameworks ◽  
Rule Based ◽  
Postgraduate Students ◽  
Dominant Paradigm

Optimaalsusteooria (OT) esitasid 1990. aastate alguses Alan Prince ja Paul Smolensky. Praeguseks on OTst saanud enim kasutatav teooria fonoloogias. Tegemist on generatiivse teooria edasiarendusega. Artiklis tutvustan lühidalt optimaalsusteooria põhiseisukohti, samuti mõningaid varasemaid teooriaid, mis on OTga seotud. Pööran tähelepanu ka sellele, miks OTs on nähtud funktsionalistide ja formalistide lepitajat, ning milliseid muutusi uurimisprobleemide valikul on OT levik kaasa toonud. Väiteid ilmestab lihtne näide eesti keele kaasaütleva käände kujunemisest: miks on tunnuseks kujunenud ‑ga, mitte ‑kka ega -ks.Optimality Theory in phonology. Optimality Theory (OT), which has become the dominant paradigm for phonological research, was developed in the early 1990s by Alan Prince and Paul Smolensky. Compared to rule-based frameworks, OT arguably has more explanatory power. OT also gives the opportunity for the synthesis of functionalist and formalist ideas. In this paper, I introduce some main principles of OT. To illustrate how OT works, I present a somewhat simplified case study of the phonological development of Estonian comitative ending -ga (from the postposition *kansak ’with’). The aim of this paper is to introduce OT (in Estonian) to postgraduate students and researchers working within other theoretical frameworks.

scholarly journals Neutralization in Aztec Phonology – The Case of Classical Nahuatl Nasals

2016 ◽  
Vol 14 (3) ◽  
pp. 263-295
Author(s):  
Michał Kuźmicki
Keyword(s):  
Optimality Theory ◽  
Rule Based ◽  
Word Level

This article investigates nasal assimilation in Classical Nahuatl. The distribution of nasal consonants is shown to be the result of coda neutralization. It is argued that generalizations made for root and word level are disproportionate and cannot be explained through the means of rule-based phonology. It is shown that the process responsible for nasal distribution can only be accounted for by introducing derivational levels in Optimality Theory.

Implicationally Related Error Patterns and the Selection of Treatment Targets

2001 ◽  
Vol 32 (4) ◽  
pp. 257-270 ◽  
Author(s):  
Daniel A. Dinnsen ◽  
Kathleen M. O’Connor
Keyword(s):  
Case Studies ◽  
Optimality Theory ◽  
Clinical Treatment ◽  
Rule Based ◽  
Error Patterns ◽  
Treatment Targets ◽  
Principled Explanation ◽  
Selection Of

This paper compares some of the different claims that have been made concerning acquisition by traditional rule-based derivational theories and the more recent framework of optimality theory. Case studies of children with phonological delays are examined with special attention given to two seemingly independent error patterns, namely, place harmony and spirantization. Contrary to the expectations of derivational theories, these (and other) error patterns are argued to be implicationally related. Optimality theory is shown to offer a principled explanation for the facts with novel implications for clinical treatment.

scholarly journals A revised typology of opaque generalisations

Phonology ◽  
2007 ◽  
Vol 24 (2) ◽  
pp. 217-259 ◽  
Author(s):  
Eric Baković
Keyword(s):  
Recent Work ◽  
Optimality Theory ◽  
Phonological Processes ◽  
Rule Based

This paper is about opaque interactions between phonological processes in the two senses defined by Kiparsky (1971, 1973) and discussed in much recent work on the topic, most notably McCarthy (1999) :underapplicationopacity, whereby a process appears to have failed to apply in expected contexts on the surface, andoverapplicationopacity, whereby a process appears to have applied in unexpected contexts on the surface. Specifically, I demonstrate that there are three distinct types of overapplication opacity in addition to the only case discussed and properly categorised as such in the literature, counterbleeding. The analysis of each type of opacity in terms of rule-based serialism and in terms of Optimality Theory is discussed, emphasising the strengths and weaknesses of the two frameworks in each case.

scholarly journals LFG Generation from Acyclic F-Structures is NP-Hard

2021 ◽  
pp. 1-9
Author(s):  
Jürgen Wedekind ◽  
Ronald M. Kaplan
Keyword(s):  
Np Hard ◽  
Generation Problem

Abstract The universal generation problem for LFG grammars is the problem of determining whether a given grammar derives any terminal string with a given f-structure. It is known that this problem is decidable for acyclic f-structures. In this brief note, we show that for those f-structures the problem is nonetheless intractable. This holds even for grammars that are off-line parsable.

scholarly journals A Rule-ordering Theory of Blocking in Nonderived Environments

2016 ◽  
Vol 3 ◽  
Author(s):  
Ezer Rasin
Keyword(s):  
Optimality Theory ◽  
Phonological Process ◽  
Rule Based ◽  
Do So ◽  
Rule Ordering

In Nonderived Environment Blocking (NDEB), a phonological process applies across morpheme boundaries or morpheme-internally when fed by another phonological process but is otherwise blocked from applying. NDEB poses a challenge to both rule-based phonology and Optimality Theory: if P is a process that is blocked in nonderived environments, the challenge in both frameworks is to partition the set of environments of application of P into two subsets – corresponding to derived and nonderived environments – and block the application of the process precisely in nonderived environments. My goal in this paper is to show that NDEB can be reduced to rule ordering. I will do so by presenting a rule-ordering theory of NDEB that uses morpheme structure rules. Every rule P that is blocked in nonderived environments will be ordered after a morpheme structure rule R that removes P’s environments of application. Since morpheme structure rules apply to URs of individual morphemes (which correspond to nonderived environments), R will prevent P from applying precisely in nonderived environments.

scholarly journals Anti-structure preservation effects in optimality theory

2003 ◽  
Vol 32 ◽  
pp. 87-110
Author(s):  
Tracy Alan Hall
Keyword(s):  
Optimality Theory ◽  
Ad Hoc ◽  
Rule Based ◽  
Structure Preservation ◽  
Significant Point

The present study examines a particular kind of rule blockage – referred to below as an 'antistructure-preservation effect'. An anti-structure-preservation effect occurs if some language has a process which is preempted from going into effect if some sequence of sounds [XY] would occur on the surface, even though other words in the language have [XY] sequences (which are underlyingly /XY/). It will be argued below that anti-structure-preservation effects can be captured in Optimality Theory in terms of a general ranking involving FAITH and MARKEDNESS constraints and that individual languages invoke a specific instantiation of this ranking. A significant point made below is that while anti-structure-preservation effects can be handled straightforwardly in terms of constraint rankings they typically require ad hoc rule-specific conditions in rule-based approaches.  

scholarly journals Hybrid Opacity in Berbice Dutch Creole

2014 ◽  
Vol 1 (1) ◽  
Author(s):  
Michael Dow
Keyword(s):  
Experimental Design ◽  
Recent Work ◽  
Optimality Theory ◽  
Mutual Exclusivity ◽  
Rule Based ◽  
Output Mapping ◽  
Place Assimilation ◽  
Single Input

<p>Recent work on opacity calls attention to the need for a refined taxonomy (e.g. Baković 2007, 2011), though the mutual exclusivity of the two major kinds of opaque interactions, underapplication and overapplication, remains unquestioned. No interaction has, until now, been reported to display both effects for a single input to output mapping. I present one case from Berbice Dutch Creole (hereafter Berbice) where, depending on the analysis, nasal place assimilation simultaneously underapplies and overapplies, due to an interaction with consonant deletion. In this paper, I present several possible analyses of the Berbice data in rule-based serialism and Optimality Theory with Candidate Chains (McCarthy 2007) and compare the claims these frameworks make on the interaction’s classification. I also discuss the theoretical implications of hybrid opacity and how it may fit within the larger taxonomy of opacity. Finally, I lay the foundation for further work on the phenomenon by presenting a generalized template and a possible experimental design.</p>

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