A Catalog for Prediction-Preserving Reducibility with Membership Queries on Formal Languages
نویسندگان
چکیده
This paper presents several results of prediction-preserving reducibility with membership queries (pwm-reducibility) on formal languages. We mainly deal with two kinds of concept classes, simple CFGs and finite unions of regular pattern languages. For the former, we show that DNF formulas are pwm-reducible to CFGs that is sequential or that contains at most one nonterminal. For the latter, on the other hand, we show that both bounded finite unions of regular pattern languages and unbounded finite unions of substring pattern languages are pwmreducible to DFAs, while DNF formulas are pwm-reducible to unbounded finite unions of regular pattern languages.
منابع مشابه
Prediction-Preserving Reducibility with Membership Queries on Formal Languages
This paper presents the prediction-preserving reducibility with membership queries (pwm-reducibility) on formal languages, in particular, simple CFGs and finite unions of regular pattern languages. For the former, we mainly show that DNF formulas are pwm-reducible to CFGs that is sequential or that contains at most one nonterminal. For the latter, we show that both bounded finite unions of regu...
متن کاملSparse Variations and Reducibility among Prediction Problems Authors :
We investigate the relationship between two di erent notions of reducibility among prediction (learning) problems within the distribution-free learning model of Valiant (PAC learning model [7, 2].) The notions of reducibility we consider are the analogues for prediction problems of the many-one reducibility and of the Turing reducibility. The former is the notion of prediction preserving reduci...
متن کاملReductions among prediction problems: on the difficulty of predicting automata
Consider the following question: Given examples of words accepted and rejected by an unknown automaton, is there an algorithm that in a feasible amount of time will learn to predict which words will be accepted by the automaton? We develop a notion of prediction-preserving reducibility, and show that if DFAs are predictable, then so are all languages in logspace. In particular, the predictabili...
متن کاملA Note on the Power of Extra Queries to Membership Comparable Sets
A language is called k-membership comparable if there exists a polynomial-time algorithm that excludes for any k words one of the 2 possibilities for their characteristic string. It is known that all membership comparable languages can be reduced to some P-selective language with polynomially many adaptive queries. We show however that for all k there exists a (k + 1)-membership comparable set ...
متن کاملLanguages that Are Easier than their Proofs
A basic question about NP is whether or not search reduces in polynomial time to decision. We indicate that the answer is negative: under a complexity assumption (that deterministic and nondeterministic double-exponential time are unequal) we construct a language in NP for which search does not reduce to decision. These ideas extend in a natural way to interactive proofs and program checking. U...
متن کامل