How NP got a new definition: a survey of probabilistically checkable proofs
نویسنده
چکیده
We survey a collective achievement of a group of researchers: the PCP Theorems. They give new definitions of the class NP, and imply that computing approximate solutions to many NP-hard problems is itself NP-hard. Techniques developed to prove them have had many other consequences. 2000 Mathematics Subject Classification: 68Q10, 68Q15, 68Q17, 68Q25.
منابع مشابه
Probabilistically Checkable Proofs: A Primer
Probabilistically checkable proofs are proofs that can checked probabilistically by reading very few bits of the proof. Roughly ten years back it was shown that proofs could be made probabilistically checkable with a modest increase in their size. While the initial proofs were a little too complex, a recent proof due to Irit Dinur gives a dramatically simple (and radically new) construction of ...
متن کاملOn Dinur’s Proof of the Pcp Theorem
Probabilistically checkable proofs are proofs that can be checked probabilistically by reading very few bits of the proof. In the early 1990s, it was shown that proofs could be transformed into probabilistically checkable ones with only a modest increase in their length. The initial transformations, though elementary, were a little too complex. A recent work due to Irit Dinur gives a dramatical...
متن کاملNotes on Complexity Theory Last updated : November , 2011 Lecture 21
Work on interactive proof systems motivates further exploration of non-interactive proof systems (e.g., the class NP). One specific question is: how many bits of the proof does the verifier need to read? Note that in the usual certificate-based definition of NP, the deterministic “verifier” reads the entire certificate, and correctness and soundness hold with probability 1. If we allow the veri...
متن کاملProbabilistically Checkable Proofs and Approximating Solutions to Hard Problems
2 A Brief Introduction to Theory of Computation 3 2.1 Some Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Modelling Computation Turing Machines . . . . . . . . . . . . 3 2.3 NP Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 Sample NP Problems . . . . . . . . . . . . . . . . . . . . . . . . 7 2.5 Optimizations for NP Problems . . . . . . . . . . . . ...
متن کاملA Note on Almost Perfect Probabilistically Checkable Proofs of Proximity
Probabilistically checkable proofs of proximity (PCPP) are proof systems where the verifier is given a 3SAT formula, but has only oracle access to an assignment and a proof. The verifier accepts a satisfying assignment with a valid proof, and rejects (with high enough probability) an assignment that is far from all satisfying assignments (for any given proof). In this work, we focus on the type...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره cs.CC/0304038 شماره
صفحات -
تاریخ انتشار 2002