Efficient learning algorithms yield circuit lower bounds
نویسندگان
چکیده
منابع مشابه
Efficient Learning Algorithms Yield Circuit Lower Bounds
We describe a new approach for understanding the difficulty of designing efficient learning algorithms. We prove that the existence of an efficient learning algorithm for a circuit class C in Angluin’s model of exact learning from membership and equivalence queries or in Valiant’s PAC model yields a lower bound against C. More specifically, we prove that any subexponential time, determinstic ex...
متن کاملAlgorithms versus Circuit Lower Bounds
Different techniques have been used to prove several transference theorems of the form “nontrivial algorithms for a circuit class C yield circuit lower bounds against C”. In this survey we revisit many of these results. We discuss how circuit lower bounds can be obtained from derandomization, compression, learning, and satisfiability algorithms. We also cover the connection between circuit lowe...
متن کاملConspiracies Between Learning Algorithms, Circuit Lower Bounds, and Pseudorandomness
We prove several results giving new and stronger connections between learning theory, circuit complexity and pseudorandomness. Let C be any typical class of Boolean circuits, and C[s(n)] denote n-variable C-circuits of size ≤ s(n). We show: Learning Speedups. If C[poly(n)] admits a randomized weak learning algorithm under the uniform distribution with membership queries that runs in time 2/n, t...
متن کاملBoolean Circuit Lower Bounds
The lectures are devoted to boolean circuit lower bounds. We consider circuits with gates ∧,∨,¬. Suppose L ∈ {0, 1}∗ is a language. Let Ln = L∩{0, 1}. We say that L is computed by a family of circuits C1, C2, . . . if on an input x = (x1, . . . , xn), Cn(x) is 1 when x ∈ Ln and is 0 when x / ∈ Ln. For a circuit C, we define size(C) to be the number of edges in the graph representing C, and dept...
متن کاملIronic Complicity: Satisfiability Algorithms and Circuit Lower Bounds
I discuss recent progress in developing and exploiting connections between SAT algorithms and circuit lower bounds. The centrepiece of the article is Williams’ proof that NEXP 6⊆ ACC, which proceeds via a new algorithm for ACC-SAT beating brute-force search. His result exploits a formal connection from non-trivial SAT algorithms to circuit lower bounds. I also discuss various connections in the...
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: Journal of Computer and System Sciences
سال: 2009
ISSN: 0022-0000
DOI: 10.1016/j.jcss.2008.07.006