期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2016
卷号：2016
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：In the setting of non-commutative arithmetic computations, we define a class of circuits that gener- alize algebraic branching programs (ABP). This model is called unambiguous because it captures the polynomials in which all monomials are computed in a similar way (that is, all the parse trees are iso- morphic). We show that unambiguous circuits of polynomial size can compute polynomials that require ABPs of exponential size, and that they are incomparable with skew circuits. Generalizing a result of Nisan [17] on ABPs, we provide an exact characterization of the complexity of any polynomial in our model, and use it to prove exponential lower bounds for explicit polynomials such as the determinant. Finally, we give a deterministic polynomial-time algorithm for polynomial identity testing (PIT) on unambiguous circuits over R and C , thus providing the largest class of circuits so far in a non-commutative setting for which we can derandomize PIT
