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

On the origin of the λ\lambda-transition in liquid Sulphur

Developing a novel experimental technique, we applied photon correlation spectroscopy using infrared radiation in liquid Sulphur around $T_\lambda$, i.e. in the temperature range where an abrupt increase in viscosity by four orders of magnitude is observed upon heating within few degrees. This allowed us - overcoming photo-induced and absorption effects at visible wavelengths - to reveal a chain relaxation process with characteristic time in the ms range. These results do rehabilitate the validity of the Maxwell relation in Sulphur from an apparent failure, allowing rationalizing the mechanical and thermodynamic behavior of this system within a viscoelastic scenario.Comment: 5 pages, 4 eps figures, accepted in Phys. Rev. Let

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

Zero Knowledge Protocols from Succinct Constraint Detection

We study the problem of constructing proof systems that achieve both soundness and zero knowledge unconditionally (without relying on intractability assumptions). Known techniques for this goal are primarily *combinatorial*, despite the fact that constructions of interactive proofs (IPs) and probabilistically checkable proofs (PCPs) heavily rely on *algebraic* techniques to achieve their properties. We present simple and natural modifications of well-known algebraic IP and PCP protocols that achieve unconditional (perfect) zero knowledge in recently introduced models, overcoming limitations of known techniques. 1. We modify the PCP of Ben-Sasson and Sudan [BS08] to obtain zero knowledge for NEXP in the model of Interactive Oracle Proofs [BCS16,RRR16], where the verifier, in each round, receives a PCP from the prover. 2. We modify the IP of Lund, Fortnow, Karloff, and Nisan [LFKN92] to obtain zero knowledge for #P in the model of Interactive PCPs [KR08], where the verifier first receives a PCP from the prover and then interacts with him. The simulators in our zero knowledge protocols rely on solving a problem that lies at the intersection of coding theory, linear algebra, and computational complexity, which we call the *succinct constraint detection* problem, and consists of detecting dual constraints with polynomial support size for codes of exponential block length. Our two results rely on solutions to this problem for fundamental classes of linear codes: * An algorithm to detect constraints for Reed--Muller codes of exponential length. This algorithm exploits the Raz--Shpilka [RS05] deterministic polynomial identity testing algorithm, and shows, to our knowledge, a first connection of algebraic complexity theory with zero knowledge. * An algorithm to detect constraints for PCPs of Proximity of Reed--Solomon codes [BS08] of exponential degree. This algorithm exploits the recursive structure of the PCPs of Proximity to show that small-support constraints are locally spanned by a small number of small-support constraints

Non-autistic observers both detect and demonstrate the double empathy problem when evaluating interactions between autistic and non-autistic adults

Consistent with a “double empathy” framework, autistic adults often experience better interaction with autistic compared with non-autistic partners. Here, we examined whether non-autistic observers detect differences in autistic interactions relative to non-autistic and mixed ones. Non-autistic adults (N = 102) rated the interaction quality and traits of 42 autistic and 44 non-autistic male participants interacting in same or mixed-neurotype dyads. Non-autistic interactions and participants were evaluated most positively, with participants rated more favorably when interacting with non-autistic partners and rated as less intelligent and awkward when interacting with autistic partners. Observers perceived mixed interactions as the least successful overall. Whereas non-autistic interactions were rated as smoother and more enjoyable than mixed interactions, they were not rated differently from autistic interactions on any measure of interaction quality. Observers also perceived that non-autistic participants but not autistic participants disclosed more to non-autistic partners. However, they evaluated autistic participants more negatively than their partners in the interaction evaluated them; they disproportionately underestimated trust and intelligence ratings made by autistic participants; and they and reported lower social interest in participants than did the autistic and non-autistic people in the interactions. Collectively, these findings indicate that non-autistic adults both detect and demonstrate the double empathy problem when observing social interactions involving autistic people

Regions of High Out-Of-Hospital Cardiac Arrest Incidence and Low Bystander CPR Rates in Victoria, Australia

BACKGROUND: Out-of-hospital cardiac arrest (OHCA) remains a major public health issue and research has shown that large regional variation in outcomes exists. Of the interventions associated with survival, the provision of bystander CPR is one of the most important modifiable factors. The aim of this study is to identify census areas with high incidence of OHCA and low rates of bystander CPR in Victoria, Australia. METHODS: We conducted an observational study using prospectively collected population-based OHCA data from the state of Victoria in Australia. Using ArcGIS (ArcMap 10.0), we linked the location of the arrest using the dispatch coordinates (longitude and latitude) to Victorian Local Government Areas (LGAs). We used Bayesian hierarchical models with random effects on each LGA to provide shrunken estimates of the rates of bystander CPR and the incidence rates. RESULTS: Over the study period there were 31,019 adult OHCA attended, of which 21,436 (69.1%) cases were of presumed cardiac etiology. Significant variation in the incidence of OHCA among LGAs was observed. There was a 3 fold difference in the incidence rate between the lowest and highest LGAs, ranging from 38.5 to 115.1 cases per 100,000 person-years. The overall rate of bystander CPR for bystander witnessed OHCAs was 62.4%, with the rate increasing from 56.4% in 2008-2010 to 68.6% in 2010-2013. There was a 25.1% absolute difference in bystander CPR rates between the highest and lowest LGAs. CONCLUSION: Significant regional variation in OHCA incidence and bystander CPR rates exists throughout Victoria. Regions with high incidence and low bystander CPR participation can be identified and would make suitable targets for interventions to improve CPR participation rates

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 $O(\log^2 n)$; it can be produced with $O(n \log n)$ field operations and verified with $O(n)$. 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