1,289 research outputs found
Testing formula satisfaction
We study the query complexity of testing for properties defined by read once formulae, as instances of massively parametrized properties, and prove several testability and non-testability results. First we prove the testability of any property accepted by a Boolean read-once formula involving any bounded arity gates, with a number of queries exponential in \epsilon and independent of all other parameters. When the gates are limited to being monotone, we prove that there is an estimation algorithm, that outputs an approximation of the distance of the input from
satisfying the property. For formulae only involving And/Or gates, we provide a more efficient test whose query complexity is only quasi-polynomial in \epsilon. On the other hand we show that such testability results do not hold in general for formulae over non-Boolean alphabets; specifically we construct a property defined by a read-once arity 2 (non-Boolean) formula over alphabets of size 4, such that any 1/4-test for it requires a number of queries depending on the formula size
A PCP Characterization of AM
We introduce a 2-round stochastic constraint-satisfaction problem, and show
that its approximation version is complete for (the promise version of) the
complexity class AM. This gives a `PCP characterization' of AM analogous to the
PCP Theorem for NP. Similar characterizations have been given for higher levels
of the Polynomial Hierarchy, and for PSPACE; however, we suggest that the
result for AM might be of particular significance for attempts to derandomize
this class.
To test this notion, we pose some `Randomized Optimization Hypotheses'
related to our stochastic CSPs that (in light of our result) would imply
collapse results for AM. Unfortunately, the hypotheses appear over-strong, and
we present evidence against them. In the process we show that, if some language
in NP is hard-on-average against circuits of size 2^{Omega(n)}, then there
exist hard-on-average optimization problems of a particularly elegant form.
All our proofs use a powerful form of PCPs known as Probabilistically
Checkable Proofs of Proximity, and demonstrate their versatility. We also use
known results on randomness-efficient soundness- and hardness-amplification. In
particular, we make essential use of the Impagliazzo-Wigderson generator; our
analysis relies on a recent Chernoff-type theorem for expander walks.Comment: 18 page
Arya: Nearly linear-time zero-knowledge proofs for correct program execution
There have been tremendous advances in reducing interaction, communication and verification time in zero-knowledge proofs but it remains an important challenge to make the prover efficient. We construct the first zero-knowledge proof of knowledge for the correct execution of a program on public and private inputs where the prover computation is nearly linear time. This saves a polylogarithmic factor in asymptotic performance compared to current state of the art proof systems.
We use the TinyRAM model to capture general purpose processor computation. An instance consists of a TinyRAM program and public inputs. The witness consists of additional private inputs to the program. The prover can use our proof system to convince the verifier that the program terminates with the intended answer within given time and memory bounds. Our proof system has perfect completeness, statistical special honest verifier zero-knowledge, and computational knowledge soundness assuming linear-time computable collision-resistant hash functions exist. The main advantage of our new proof system is asymptotically efficient prover computation. The prover’s running time is only a superconstant factor larger than the program’s running time in an apples-to-apples comparison where the prover uses the same TinyRAM model. Our proof system is also efficient on the other performance parameters; the verifier’s running time and the communication are sublinear in the execution time of the program and we only use a log-logarithmic number of rounds
Fractal: Post-Quantum and Transparent Recursive Proofs from Holography
We present a new methodology to efficiently realize recursive composition of succinct non-interactive arguments of knowledge (SNARKs). Prior to this work, the only known methodology relied on pairing-based SNARKs instantiated on cycles of pairing-friendly elliptic curves, an expensive algebraic object. Our methodology does not rely on any special algebraic objects and, moreover, achieves new desirable properties: it is *post-quantum* and it is *transparent* (the setup is public coin).
We exploit the fact that recursive composition is simpler for SNARKs with *preprocessing*, and the core of our work is obtaining a preprocessing zkSNARK for rank-1 constraint satisfiability (R1CS) that is post-quantum and transparent. We obtain this latter by establishing a connection between holography and preprocessing in the random oracle model, and then constructing a holographic proof for R1CS.
We experimentally validate our methodology, demonstrating feasibility in practice
Aurora: Transparent Succinct Arguments for R1CS
We design, implement, and evaluate a zkSNARK for Rank-1 Constraint Satisfaction (R1CS), a widely-deployed NP-complete language that is undergoing standardization. Our construction uses a transparent setup, is plausibly post-quantum secure, and uses lightweight cryptography. A proof attesting to the satisfiability of n constraints has size ; it can be produced with field operations and verified with . At 128 bits of security, proofs are less than 130kB even for several million constraints, more than 20x shorter than prior zkSNARK with similar features.
A key ingredient of our construction is a new Interactive Oracle Proof (IOP) for solving a *univariate* analogue of the classical sumcheck problem [LFKN92], originally studied for *multivariate* polynomials. Our protocol verifies the sum of entries of a Reed--Solomon codeword over any subgroup of a field.
We also provide libiop, an open-source library for writing IOP-based arguments, in which a toolchain of transformations enables programmers to write new arguments by writing simple IOP sub-components. We have used this library to specify our construction and prior ones
Brief report: how adolescents with ASD process social information in complex scenes. Combining evidence from eye movements and verbal descriptions
We investigated attention, encoding and processing of social aspects of complex photographic scenes. Twenty-four high-functioning adolescents (aged 11–16) with ASD and 24 typically developing matched control participants viewed and then described a series of scenes, each containing a person. Analyses of eye movements and verbal descriptions provided converging evidence that both groups displayed general interest in the person in each scene but the salience of the person was reduced for the ASD participants. Nevertheless, the verbal descriptions revealed that participants with ASD frequently processed the observed person’s emotion or mental state without prompting. They also often mentioned eye-gaze direction, and there was evidence from eye movements and verbal descriptions that gaze was followed accurately. The combination of evidence from eye movements and verbal descriptions provides a rich insight into the way stimuli are processed overall. The merits of using these methods within the same paradigm are discussed
Transcriptional Profiling of Peripheral Blood Mononuclear Cells in Pancreatic Cancer Patients Identifies Novel Genes with Potential Diagnostic Utility
Background: It is well known that many malignancies, including pancreatic cancer (PC), possess the ability to evade the immune system by indirectly downregulating the mononuclear cell machinery necessary to launch an effective immune response. This knowledge, in conjunction with the fact that the trancriptome of peripheral blood mononuclear cells has been shown to be altered in the context of many diseases, including renal cell carcinoma, lead us to study if any such alteration in gene expression exists in PC as it may have diagnostic utility. Methods and Findings: PBMC samples from 26 PC patients and 33 matched healthy controls were analyzed by whole genome cDNA microarray. Three hundred eighty-three genes were found to be significantly different between PC and healthy controls, with 65 having at least a 1.5 fold change in expression. Pathway analysis revealed that many of these genes fell into pathways responsible for hematopoietic differentiation, cytokine signaling, and natural killer (NK) cell and CD8+ T-cell cytotoxic response. Unsupervised hierarchical clustering analysis identified an eight-gene predictor set, consisting of SSBP2, Ube2b-rs1, CA5B, F5, TBC1D8, ANXA3, ARG1, and ADAMTS20, that could distinguish PC patients from healthy controls with an accuracy of 79% in a blinded subset of samples from treatment naïve patients, giving a sensitivity of 83% and a specificity of 75%. Conclusions: In summary, we report the first in-depth comparison of global gene expression profiles of PBMCs between PC patients and healthy controls. We have also identified a gene predictor set that can potentially be developed further for use in diagnostic algorithms in PC. Future directions of this research should include analysis of PBMC expression profiles in patients with chronic pancreatitis as well as increasing the number of early-stage patients to assess the utility of PBMCs in the early diagnosis of PC. © 2011 Baine et al
The Natural Protective Mechanism Against Hyperglycemia in Vascular Endothelial Cells: Roles of the Lipid Peroxidation Product 4-Hydroxydodecadienal and Peroxisome Proliferator–Activated Receptor δ
Sonic: Zero-Knowledge SNARKs from Linear-Size Universal and Updateable Structured Reference Strings
Ever since their introduction, zero-knowledge proofs have become an important tool for addressing privacy and scalability concerns in a variety of applications. In many systems each client downloads and verifies every new proof, and so proofs must be small and cheap to verify. The most practical schemes require either a trusted setup, as in (pre-processing) zk-SNARKs, or verification complexity that scales linearly with the complexity of the relation, as in Bulletproofs. The structured reference strings required by most zk-SNARK schemes can be constructed with multi-party computation protocols, but the resulting parameters are specific to an individual relation. Groth et al. discovered a zk-SNARK protocol with a universal structured reference string that is also updatable, but the string scales quadratically in the size of the supported relations.
Here we describe a zero-knowledge SNARK, Sonic, which supports a universal and continually updatable structured reference string that scales linearly in size. We also describe a generally useful technique in which untrusted "helpers" can compute advice that allows batches of proofs to be verified more efficiently. Sonic proofs are constant size, and in the "helped" batch verification context the marginal cost of verification is comparable with the most efficient SNARKs in the literature
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