Complexity of Terms , Composition , and Hypersubstitution
نویسندگان
چکیده
We consider four useful measures of the complexity of a term: themaximumdepth (usually called the depth), the minimum depth, the variable count, and the operation count. For each of these, we produce a formula for the complexity of the composition Sn m(s,t1, . . . , tn) in terms of the complexity of the inputs s, t1, . . . , tn. As a corollary, we also obtain formulas for the complexity of σ̂ [t] in terms of the complexity of t when t is a compound term and σ is a hypersubstitution. We then apply these formulas to the theory of M-solid varieties, examining the k-normalization chains of a variety with respect to the four complexity measures.
منابع مشابه
Complexity of Hypersubstitutions and Lattices of Varieties
Hypersubstitutions are mappings which map operation symbols to terms. The set of all hypersubstitutions of a given type forms a monoid with respect to the composition of operations. Together with a second binary operation, to be written as addition, the set of all hypersubstitutions of a given type forms a left-seminearring. Monoids and leftseminearrings of hypersubstitutions can be used to des...
متن کاملTOEFL iBT integrated speaking tests: a comparison of test-takers' performance in terms of complexity, accuracy, and fluency
This study compares three integrated tasks of the TOEFL iBT speaking subtest in terms of complexity, accuracy, and fluency. To this end, a group of TOEFL iBT Iranian candidates took a simulated TOEFL iBT some days prior to their real exam. The collected oral responses were first transcribed and then quantified using software such as ‘Syllable Counter’ and ‘Coh-Metrix3’ for fluency and complexit...
متن کاملM -hyperquasi-identities of Finite Algebras *
In [4] (see [2]) the notion of a hypersubstitution of a given type and the notion of a derived variety D(V ) of a given variety V of a fixed type τ were invented. Suitable hyperequational calculus appeared as a modification of G. Birkhoff calculus with additional rule called hypersubstitution rule (6). In Graczyńska E. and Schweigert D. [6] we considered further generalization to M-hyperquasiva...
متن کاملImproving Iranian Intermediate EFL Learners’ Oral Narrative Task Performance in Terms of Accuracy, Fluency and Complexity by Awareness Raising Through Semantic Fields
The effects different awareness-raising techniques might have on language learners’ performance have been studied by many researchers. The present study specifically focused on improving EFL learners’ oral narrative task performance in terms of accuracy, fluency and complexity by awareness raising through semantic fields. The participants in the study included 40 intermediate learners whose ini...
متن کاملInput-induced Variation in EFL Learners’ Oral Production in Terms of Complexity, Accuracy, and Fluency
Researchers have extensively studied phenomena that affect a second language learner’s oral production while there is scant evidence about input-related factors. Accordingly, the present study sought to investigate how variation in oral production is caused by the input they receive from different course materials. To this end, the study included a micro-evaluation study of three course materia...
متن کامل