Some Applications of Coding Theory in Computational Complexity

Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable error-correcting codes, and their applications to complexity theory and to cryptography. Locally decodable codes are error-correcting codes with sub-linear time error-correcting algorithms. They are related to private information retrieval (a type of cryptographic protocol), and they are used in average-case complexity and to construct ``hard-core predicates'' for one-way permutations. Locally testable codes are error-correcting codes with sub-linear time error-detection algorithms, and they are the combinatorial core of probabilistically checkable proofs

DFT and BIST of a multichip module for high-energy physics experiments

Engineers at Politecnico di Torino designed a multichip module for high-energy physics experiments conducted on the Large Hadron Collider. An array of these MCMs handles multichannel data acquisition and signal processing. Testing the MCM from board to die level required a combination of DFT strategie

Quantum Locally Testable Code with Exotic Parameters

In this paper, we present a few simple constructions of quantum locally testable codes that achieve interesting parameters which were previously unknown. We introduce an operation which we give the name check product, and show how this operation gives rise to quantum locally testable codes of constant soundness and linear rate, with varying distance and locality

AFSM-based deterministic hardware TPG

This paper proposes a new approach for designing a cost-effective, on-chip, hardware pattern generator of deterministic test sequences. Given a pre-computed test pattern (obtained by an ATPG tool) with predetermined fault coverage, a hardware Test Pattern Generator (TPG) based on Autonomous Finite State Machines (AFSM) structure is synthesized to generate it. This new approach exploits "don't care" bits of the deterministic test patterns to lower area overhead of the TPG. Simulations using benchmark circuits show that the hardware components cost is considerably less when compared with alternative solution

Experimental device-independent certified randomness generation with an instrumental causal structure

The intrinsic random nature of quantum physics offers novel tools for the generation of random numbers, a central challenge for a plethora of fields. Bell non-local correlations obtained by measurements on entangled states allow for the generation of bit strings whose randomness is guaranteed in a device-independent manner, i.e. without assumptions on the measurement and state-generation devices. Here, we generate this strong form of certified randomness on a new platform: the so-called instrumental scenario, which is central to the field of causal inference. First, we theoretically show that certified random bits, private against general quantum adversaries, can be extracted exploiting device-independent quantum instrumental-inequality violations. To that end, we adapt techniques previously developed for the Bell scenario. Then, we experimentally implement the corresponding randomness-generation protocol using entangled photons and active feed-forward of information. Moreover, we show that, for low levels of noise, our protocol offers an advantage over the simplest Bell-nonlocality protocol based on the Clauser-Horn-Shimony-Holt inequality.Comment: Modified Supplementary Information: removed description of extractor algorithm introduced by arXiv:1212.0520. Implemented security of the protocol against general adversarial attack

On Buffon Machines and Numbers

The well-know needle experiment of Buffon can be regarded as an analog (i.e., continuous) device that stochastically "computes" the number 2/pi ~ 0.63661, which is the experiment's probability of success. Generalizing the experiment and simplifying the computational framework, we consider probability distributions, which can be produced perfectly, from a discrete source of unbiased coin flips. We describe and analyse a few simple Buffon machines that generate geometric, Poisson, and logarithmic-series distributions. We provide human-accessible Buffon machines, which require a dozen coin flips or less, on average, and produce experiments whose probabilities of success are expressible in terms of numbers such as, exp(-1), log 2, sqrt(3), cos(1/4), aeta(5). Generally, we develop a collection of constructions based on simple probabilistic mechanisms that enable one to design Buffon experiments involving compositions of exponentials and logarithms, polylogarithms, direct and inverse trigonometric functions, algebraic and hypergeometric functions, as well as functions defined by integrals, such as the Gaussian error function.Comment: Largely revised version with references and figures added. 12 pages. In ACM-SIAM Symposium on Discrete Algorithms (SODA'2011

Plug & Test at System Level via Testable TLM Primitives

With the evolution of Electronic System Level (ESL) design methodologies, we are experiencing an extensive use of Transaction-Level Modeling (TLM). TLM is a high-level approach to modeling digital systems where details of the communication among modules are separated from the those of the implementation of functional units. This paper represents a first step toward the automatic insertion of testing capabilities at the transaction level by definition of testable TLM primitives. The use of testable TLM primitives should help designers to easily get testable transaction level descriptions implementing what we call a "Plug & Test" design methodology. The proposed approach is intended to work both with hardware and software implementations. In particular, in this paper we will focus on the design of a testable FIFO communication channel to show how designers are given the freedom of trading-off complexity, testability levels, and cos