Building Above Read-Once Polynomials: Identity Testing and Hardness of Representation
نویسندگان
چکیده
منابع مشابه
Isomorphism testing of read-once functions and polynomials
In this paper, we study the isomorphism testing problem of formulas in the Boolean and arithmetic settings. We show that isomorphism testing of Boolean formulas in which a variable is read at most once (known as read-once formulas) is complete for log-space. In contrast, we observe that the problem becomes polynomial time equivalent to the graph isomorphism problem, when the input formulas can ...
متن کاملA Polynomial Time Deterministic Algorithm for Identity Testing Read-Once Polynomials
The polynomial identity testing problem, or PIT, asks how we can decide if a polynomial is equivalent to zero. A read-once polynomial (ROP) is a polynomial over some field that can be expressed with an arithmetic formula where each variable appears at most once. We construct a deterministic polynomial time algorithm for identity testing a black-box ROP. In particular, we show that for a read-on...
متن کاملDeterministic Identity Testing of Read-Once Algebraic Branching Programs
In this paper we study polynomial identity testing of sums of k read-once algebraic branching programs (Σk-RO-ABPs), generalizing the work of Shpilka and Volkovich [1, 2], who considered sums of k read-once formulas (Σk-RO-formulas). We show that Σk-RO-ABPs are strictly more powerful than Σk-RO-formulas, for any k ≤ ⌊n/2⌋, where n is the number of variables. Nevertheless, as a starting observat...
متن کاملDeterministic Identity Testing for Sum of Read Once ABPs
A read once ABP is an arithmetic branching program with each variable occurring in at most one layer. We give the first polynomial time whitebox identity test for a polynomial computed by a sum of constantly many ROABPs. We also give a corresponding blackbox algorithm with quasi-polynomial time complexity, i.e. n. The motivating special case of this model is sum of constantly many set-multiline...
متن کاملPolynomial identity testing of read-once oblivious algebraic branching programs
We study the problem of obtaining efficient, deterministic, black-box polynomial identity testing algorithms (PIT) for algebraic branching programs (ABPs) that are read-once and oblivious. This class has an efficient, deterministic, white-box polynomial identity testing algorithm (due to Raz and Shpilka [RS05]), but prior to this work there was no known such black-box algorithm. The main result...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algorithmica
سال: 2015
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-015-0101-z