P(Izraz|Gramatika)

V delu definiramo verjetnostne kontekstno-neodvisne gramatike in opišemo njihovo uporabo v simbolni regresiji. Omejimo se na gramatike, ki tvorijo algebrajske izraze in natančno definiramo izraz. Motiviramo problem izračuna verjetnosti podanega izraza za podano gramatiko in dokažemo, da je v splošnem neodločljiv. Predstavimo nekaj posebnih primerov gramatik, ki generirajo izraze, za katere je problem algoritmično rešljiv. Podamo postopek za izračun verjetnosti podanega izraza za te posebne primere gramatik. Na koncu predstavimo verjetnostne gramatike, ki generirajo podmnožice grup. We define probability context-free grammars and describe their use for symbolic regression. We study grammars that generate algebraic expressions and meticulously define an expression. We show that calculating the probability of a given expression for a given grammar is generally undecidable. We overview specific grammars for generating expressions, where an algorithm for calculating the probability of a given expression exists. For those example grammars, we present an algorithm for calculating the probability of a given expression. At last, we present probabilistic grammars for generating elements from groups.