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**Published in:** LIPIcs, Volume 256, 4th Symposium on Foundations of Responsible Computing (FORC 2023)

Prediction algorithms assign scores in [0,1] to individuals, often interpreted as "probabilities" of a positive outcome, for example, of repaying a loan or succeeding in a job. Success, however, rarely depends only on the individual: it is a function of the individual’s interaction with the environment, past and present. Environments do not treat all demographic groups equally.
We initiate the study of corrective transformations τ that map predictors of success in the real world to predictors in a better world. In the language of algorithmic fairness, letting p^* denote the true probabilities of success in the real, unfair, world, we characterize the transformations τ for which it is feasible to find a predictor q̃ that is indistinguishable from τ(p^*). The problem is challenging because we do not have access to probabilities or even outcomes in a better world. Nor do we have access to probabilities p^* in the real world. The only data available for training are outcomes from the real world.
We obtain a complete characterization of when it is possible to learn predictors that are indistinguishable from τ(p^*), in the form of a simple-to-state criterion describing necessary and sufficient conditions for doing so. This criterion is inextricably bound with the very existence of uncertainty.

Cynthia Dwork, Omer Reingold, and Guy N. Rothblum. From the Real Towards the Ideal: Risk Prediction in a Better World. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 1:1-1:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{dwork_et_al:LIPIcs.FORC.2023.1, author = {Dwork, Cynthia and Reingold, Omer and Rothblum, Guy N.}, title = {{From the Real Towards the Ideal: Risk Prediction in a Better World}}, booktitle = {4th Symposium on Foundations of Responsible Computing (FORC 2023)}, pages = {1:1--1:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-272-3}, ISSN = {1868-8969}, year = {2023}, volume = {256}, editor = {Talwar, Kunal}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2023.1}, URN = {urn:nbn:de:0030-drops-179224}, doi = {10.4230/LIPIcs.FORC.2023.1}, annote = {Keywords: Algorithmic Fairness, Affirmative Action, Learning, Predictions, Multicalibration, Outcome Indistinguishability} }

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**Published in:** LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Interactive proofs of proximity (IPPs) offer ultra-fast approximate verification of assertions regarding their input, where ultra-fast means that only a small portion of the input is read and approximate verification is analogous to the notion of approximate decision that underlies property testing. Specifically, in an IPP, the prover can make the verifier accept each input in the property, but cannot fool the verifier into accepting an input that is far from the property (except for with small probability).
The verifier in an IPP system engages in two very different types of activities: interacting with an untrusted prover, and querying its input. The definition allows for arbitrary coordination between these two activities, but keeping them separate is both conceptually interesting and necessary for important applications such as addressing temporal considerations (i.e., at what time is each of the services available) and facilitating the construction of zero-knowledge schemes. In this work we embark on a systematic study of IPPs with proof-oblivious queries, where the queries should not be affected by the interaction with the prover. We assign the query and interaction activities to separate modules, and consider different limitations on their coordination.
The most strict limitation requires these activities to be totally isolated from one another; they just feed their views to a separate deciding module. We show that such systems can be efficiently emulated by standard testers.
Going to the other extreme, we only disallow information to flow from the interacting module to the querying module, but allow free information flow in the other direction. We show that extremely efficient one-round (i.e., two-message) systems of such type can be used to verify properties that are extremely hard to test (without the help of a prover). That is, the complexity of verifying can be polylogarithmic in the complexity of testing. This stands in contrast the MAPs (viewed as 1/2-round systems) in which proof-oblivious queries are as limited as our isolated model.
Our focus is on an intermediate model that allows shared randomness between the querying and interacting modules but no information flow between them. In this case we show that 1-round systems are efficiently emulated by standard testers but 3/2-round systems of extremely low complexity exist for properties that are extremely hard to test. One additional result about this model is that it can efficiently emulate any IPP for any property of low-degree polynomials.

Oded Goldreich, Guy N. Rothblum, and Tal Skverer. On Interactive Proofs of Proximity with Proof-Oblivious Queries. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 59:1-59:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{goldreich_et_al:LIPIcs.ITCS.2023.59, author = {Goldreich, Oded and Rothblum, Guy N. and Skverer, Tal}, title = {{On Interactive Proofs of Proximity with Proof-Oblivious Queries}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {59:1--59:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-263-1}, ISSN = {1868-8969}, year = {2023}, volume = {251}, editor = {Tauman Kalai, Yael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.59}, URN = {urn:nbn:de:0030-drops-175625}, doi = {10.4230/LIPIcs.ITCS.2023.59}, annote = {Keywords: Complexity Theory, Property Testing, Interactive Proofs, Interactive Proofs of Proximity, Proof-Oblivious Queries} }

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**Published in:** LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

How should we use ML-based predictions (e.g., risk of heart attack) to inform downstream binary classification decisions (e.g., undergoing a medical procedure)? When the risk estimates are perfectly calibrated, the answer is well understood: a classification problem’s cost structure induces an optimal treatment threshold j^⋆. In practice, however, predictors are often miscalibrated, and this can lead to harmful decisions. This raises a fundamental question: how should one use potentially miscalibrated predictions to inform binary decisions?
In this work, we study this question from the perspective of algorithmic fairness. Specifically, we focus on the impact of decisions on protected demographic subgroups, when we are only given a bound on the predictor’s anticipated degree of subgroup-miscalibration. We formalize a natural (distribution-free) solution concept for translating predictions into decisions: given anticipated miscalibration of α, we propose using the threshold j that minimizes the worst-case regret over all α-miscalibrated predictors, where the regret is the difference in clinical utility between using the threshold in question and using the optimal threshold in hindsight. We provide closed form expressions for j when miscalibration is measured using both expected and maximum calibration error which reveal that it indeed differs from j^⋆ (the optimal threshold under perfect calibration).

Guy N. Rothblum and Gal Yona. Decision-Making Under Miscalibration. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 92:1-92:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{rothblum_et_al:LIPIcs.ITCS.2023.92, author = {Rothblum, Guy N. and Yona, Gal}, title = {{Decision-Making Under Miscalibration}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {92:1--92:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-263-1}, ISSN = {1868-8969}, year = {2023}, volume = {251}, editor = {Tauman Kalai, Yael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.92}, URN = {urn:nbn:de:0030-drops-175951}, doi = {10.4230/LIPIcs.ITCS.2023.92}, annote = {Keywords: risk prediction, calibration, algorithmic fairness, multi-group fairness} }

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**Published in:** LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

There are growing concerns that algorithms, which increasingly make or influence important decisions pertaining to individuals, might produce outcomes that discriminate against protected groups. We study such fairness concerns in the context of a two-sided market, where there are two sets of agents, and each agent has preferences over the other set. The goal is producing a matching between the sets. Throughout this work, we use the example of matching medical residents (who we call "doctors") to hospitals. This setting has been the focus of a rich body of work. The seminal work of Gale and Shapley formulated a stability desideratum, and showed that a stable matching always exists and can be found in polynomial time.
With fairness concerns in mind, it is natural to ask: might a stable matching be discriminatory towards some of the doctors? How can we obtain a fair matching? The question is interesting both when hospital preferences might be discriminatory, and also when each hospital’s preferences are fair.
We study this question through the lens of metric-based fairness notions (Dwork et al. [ITCS 2012] and Kim et al. [ITCS 2020]). We formulate appropriate definitions of fairness and stability in the presence of a similarity metric, and ask: does a fair and stable matching always exist? Can such a matching be found in polynomial time? Can classical Gale-Shapley algorithms find such a matching? Our contributions are as follows:
- Composition failures for classical algorithms. We show that composing the Gale-Shapley algorithm with fair hospital preferences can produce blatantly unfair outcomes.
- New algorithms for finding fair and stable matchings. Our main technical contributions are efficient new algorithms for finding fair and stable matchings when: (i) the hospitals' preferences are fair, and (ii) the fairness metric satisfies a strong "proto-metric" condition: the distance between every two doctors is either zero or one. In particular, these algorithms also show that, in this setting, fairness and stability are compatible.
- Barriers for finding fair and stable matchings in the general case. We show that if the hospital preferences can be unfair, or if the metric fails to satisfy the proto-metric condition, then no algorithm in a natural class can find a fair and stable matching. The natural class includes the classical Gale-Shapley algorithms and our new algorithms.

Gili Karni, Guy N. Rothblum, and Gal Yona. On Fairness and Stability in Two-Sided Matchings. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 92:1-92:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{karni_et_al:LIPIcs.ITCS.2022.92, author = {Karni, Gili and Rothblum, Guy N. and Yona, Gal}, title = {{On Fairness and Stability in Two-Sided Matchings}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {92:1--92:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-217-4}, ISSN = {1868-8969}, year = {2022}, volume = {215}, editor = {Braverman, Mark}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.92}, URN = {urn:nbn:de:0030-drops-156880}, doi = {10.4230/LIPIcs.ITCS.2022.92}, annote = {Keywords: algorithmic fairness} }

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**Published in:** LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021)

A central question in the study of interactive proofs is the relationship between private-coin proofs, where the verifier is allowed to hide its randomness from the prover, and public-coin proofs, where the verifier’s random coins are sent to the prover. The seminal work of Goldwasser and Sipser [STOC 1986] showed how to transform private-coin proofs into public-coin ones. However, their transformation incurs a super-polynomial blowup in the running time of the honest prover.
In this work, we study transformations from private-coin proofs to public-coin proofs that preserve (up to polynomial factors) the running time of the prover. We re-consider this question in light of the emergence of doubly-efficient interactive proofs, where the honest prover is required to run in polynomial time and the verifier should run in near-linear time. Can every private-coin doubly-efficient interactive proof be transformed into a public-coin doubly-efficient proof? Adapting a result of Vadhan [STOC 2000], we show that, assuming one-way functions exist, there is no general-purpose black-box private-coin to public-coin transformation for doubly-efficient interactive proofs.
Our main result is a loose converse: if (auxiliary-input infinitely-often) one-way functions do not exist, then there exists a general-purpose efficiency-preserving transformation. To prove this result, we show a general condition that suffices for transforming a doubly-efficient private coin protocol: every such protocol induces an efficiently computable function, such that if this function is efficiently invertible (in the sense of one-way functions), then the proof can be efficiently transformed into a public-coin proof system with a polynomial-time honest prover.
This result motivates a study of other general conditions that allow for efficiency-preserving private to public coin transformations. We identify an additional (incomparable) condition to that used in our main result. This condition allows for transforming any private coin interactive proof where (roughly) it is possible to efficiently approximate the number of verifier coins consistent with a partial transcript. This allows for transforming any constant-round interactive proof that has this property (even if it is not doubly-efficient). We demonstrate the applicability of this final result by using it to transform a private-coin protocol of Rothblum, Vadhan and Wigderson [STOC 2013], obtaining a doubly-efficient public-coin protocol for verifying that a given graph is close to bipartite in a setting for which such a protocol was not previously known.

Gal Arnon and Guy N. Rothblum. On Prover-Efficient Public-Coin Emulation of Interactive Proofs. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 3:1-3:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{arnon_et_al:LIPIcs.ITC.2021.3, author = {Arnon, Gal and Rothblum, Guy N.}, title = {{On Prover-Efficient Public-Coin Emulation of Interactive Proofs}}, booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)}, pages = {3:1--3:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-197-9}, ISSN = {1868-8969}, year = {2021}, volume = {199}, editor = {Tessaro, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.3}, URN = {urn:nbn:de:0030-drops-143226}, doi = {10.4230/LIPIcs.ITC.2021.3}, annote = {Keywords: Interactive Proofs, Computational complexity, Cryptography} }

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**Published in:** LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

We consider the following question: using a source of labeled data and interaction with an untrusted prover, what is the complexity of verifying that a given hypothesis is "approximately correct"? We study interactive proof systems for PAC verification, where a verifier that interacts with a prover is required to accept good hypotheses, and reject bad hypotheses. Both the verifier and the prover are efficient and have access to labeled data samples from an unknown distribution. We are interested in cases where the verifier can use significantly less data than is required for (agnostic) PAC learning, or use a substantially cheaper data source (e.g., using only random samples for verification, even though learning requires membership queries). We believe that today, when data and data-driven algorithms are quickly gaining prominence, the question of verifying purported outcomes of data analyses is very well-motivated.
We show three main results. First, we prove that for a specific hypothesis class, verification is significantly cheaper than learning in terms of sample complexity, even if the verifier engages with the prover only in a single-round (NP-like) protocol. Moreover, for this class we prove that single-round verification is also significantly cheaper than testing closeness to the class. Second, for the broad class of Fourier-sparse boolean functions, we show a multi-round (IP-like) verification protocol, where the prover uses membership queries, and the verifier is able to assess the result while only using random samples. Third, we show that verification is not always more efficient. Namely, we show a class of functions where verification requires as many samples as learning does, up to a logarithmic factor.

Shafi Goldwasser, Guy N. Rothblum, Jonathan Shafer, and Amir Yehudayoff. Interactive Proofs for Verifying Machine Learning. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 41:1-41:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{goldwasser_et_al:LIPIcs.ITCS.2021.41, author = {Goldwasser, Shafi and Rothblum, Guy N. and Shafer, Jonathan and Yehudayoff, Amir}, title = {{Interactive Proofs for Verifying Machine Learning}}, booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)}, pages = {41:1--41:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-177-1}, ISSN = {1868-8969}, year = {2021}, volume = {185}, editor = {Lee, James R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.41}, URN = {urn:nbn:de:0030-drops-135806}, doi = {10.4230/LIPIcs.ITCS.2021.41}, annote = {Keywords: PAC learning, Fourier analysis of boolean functions, Complexity gaps, Complexity lower bounds, Goldreich-Levin algorithm, Kushilevitz-Mansour algorithm, Distribution testing} }

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**Published in:** LIPIcs, Volume 156, 1st Symposium on Foundations of Responsible Computing (FORC 2020)

It is well understood that classification algorithms, for example, for deciding on loan applications, cannot be evaluated for fairness without taking context into account. We examine what can be learned from a fairness oracle equipped with an underlying understanding of "true" fairness. The oracle takes as input a (context, classifier) pair satisfying an arbitrary fairness definition, and accepts or rejects the pair according to whether the classifier satisfies the underlying fairness truth. Our principal conceptual result is an extraction procedure that learns the underlying truth; moreover, the procedure can learn an approximation to this truth given access to a weak form of the oracle. Since every "truly fair" classifier induces a coarse metric, in which those receiving the same decision are at distance zero from one another and those receiving different decisions are at distance one, this extraction process provides the basis for ensuring a rough form of metric fairness, also known as individual fairness.
Our principal technical result is a higher fidelity extractor under a mild technical constraint on the weak oracle’s conception of fairness. Our framework permits the scenario in which many classifiers, with differing outcomes, may all be considered fair.
Our results have implications for interpretablity - a highly desired but poorly defined property of classification systems that endeavors to permit a human arbiter to reject classifiers deemed to be "unfair" or illegitimately derived.

Cynthia Dwork, Christina Ilvento, Guy N. Rothblum, and Pragya Sur. Abstracting Fairness: Oracles, Metrics, and Interpretability. In 1st Symposium on Foundations of Responsible Computing (FORC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 156, pp. 8:1-8:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dwork_et_al:LIPIcs.FORC.2020.8, author = {Dwork, Cynthia and Ilvento, Christina and Rothblum, Guy N. and Sur, Pragya}, title = {{Abstracting Fairness: Oracles, Metrics, and Interpretability}}, booktitle = {1st Symposium on Foundations of Responsible Computing (FORC 2020)}, pages = {8:1--8:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-142-9}, ISSN = {1868-8969}, year = {2020}, volume = {156}, editor = {Roth, Aaron}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FORC.2020.8}, URN = {urn:nbn:de:0030-drops-120247}, doi = {10.4230/LIPIcs.FORC.2020.8}, annote = {Keywords: Algorithmic fairness, fairness definitions, causality-based fairness, interpretability, individual fairness, metric fairness} }

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**Published in:** LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

In this work, we study notions of fairness in decision-making systems when individuals have diverse preferences over the possible outcomes of the decisions. Our starting point is the seminal work of Dwork et al. [ITCS 2012] which introduced a notion of individual fairness (IF): given a task-specific similarity metric, every pair of individuals who are similarly qualified according to the metric should receive similar outcomes. We show that when individuals have diverse preferences over outcomes, requiring IF may unintentionally lead to less-preferred outcomes for the very individuals that IF aims to protect (e.g. a protected minority group). A natural alternative to IF is the classic notion of fair division, envy-freeness (EF): no individual should prefer another individual’s outcome over their own. Although EF allows for solutions where all individuals receive a highly-preferred outcome, EF may also be overly-restrictive for the decision-maker. For instance, if many individuals agree on the best outcome, then if any individual receives this outcome, they all must receive it, regardless of each individual’s underlying qualifications for the outcome.
We introduce and study a new notion of preference-informed individual fairness (PIIF) that is a relaxation of both individual fairness and envy-freeness. At a high-level, PIIF requires that outcomes satisfy IF-style constraints, but allows for deviations provided they are in line with individuals' preferences. We show that PIIF can permit outcomes that are more favorable to individuals than any IF solution, while providing considerably more flexibility to the decision-maker than EF. In addition, we show how to efficiently optimize any convex objective over the outcomes subject to PIIF for a rich class of individual preferences. Finally, we demonstrate the broad applicability of the PIIF framework by extending our definitions and algorithms to the multiple-task targeted advertising setting introduced by Dwork and Ilvento [ITCS 2019].

Michael P. Kim, Aleksandra Korolova, Guy N. Rothblum, and Gal Yona. Preference-Informed Fairness. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 16:1-16:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{kim_et_al:LIPIcs.ITCS.2020.16, author = {Kim, Michael P. and Korolova, Aleksandra and Rothblum, Guy N. and Yona, Gal}, title = {{Preference-Informed Fairness}}, booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, pages = {16:1--16:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-134-4}, ISSN = {1868-8969}, year = {2020}, volume = {151}, editor = {Vidick, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.16}, URN = {urn:nbn:de:0030-drops-117010}, doi = {10.4230/LIPIcs.ITCS.2020.16}, annote = {Keywords: algorithmic fairness} }

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**Published in:** LIPIcs, Volume 102, 33rd Computational Complexity Conference (CCC 2018)

Consider a setting in which a prover wants to convince a verifier of the correctness of k NP statements. For example, the prover wants to convince the verifier that k given integers N_1,...,N_k are all RSA moduli (i.e., products of equal length primes). Clearly this problem can be solved by simply having the prover send the k NP witnesses, but this involves a lot of communication. Can interaction help? In particular, is it possible to construct interactive proofs for this task whose communication grows sub-linearly with k?
Our main result is such an interactive proof for verifying the correctness of any k UP statements (i.e., NP statements that have a unique witness). The proof-system uses only a constant number of rounds and the communication complexity is k^delta * poly(m), where delta>0 is an arbitrarily small constant, m is the length of a single witness, and the poly term refers to a fixed polynomial that only depends on the language and not on delta. The (honest) prover strategy can be implemented in polynomial-time given access to the k (unique) witnesses.
Our proof leverages "interactive witness verification" (IWV), a new type of proof-system that may be of independent interest. An IWV is a proof-system in which the verifier needs to verify the correctness of an NP statement using: (i) a sublinear number of queries to an alleged NP witness, and (ii) a short interaction with a powerful but untrusted prover. In contrast to the setting of PCPs and Interactive PCPs, here the verifier only has access to the raw NP witness, rather than some encoding thereof.

Omer Reingold, Guy N. Rothblum, and Ron D. Rothblum. Efficient Batch Verification for UP. In 33rd Computational Complexity Conference (CCC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 102, pp. 22:1-22:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{reingold_et_al:LIPIcs.CCC.2018.22, author = {Reingold, Omer and Rothblum, Guy N. and Rothblum, Ron D.}, title = {{Efficient Batch Verification for UP}}, booktitle = {33rd Computational Complexity Conference (CCC 2018)}, pages = {22:1--22:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-069-9}, ISSN = {1868-8969}, year = {2018}, volume = {102}, editor = {Servedio, Rocco A.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2018.22}, URN = {urn:nbn:de:0030-drops-88681}, doi = {10.4230/LIPIcs.CCC.2018.22}, annote = {Keywords: Interactive Proof, Batch Verification, Unique Solution} }

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**Published in:** LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

A proof system is called doubly-efficient if the prescribed prover strategy can be implemented in polynomial-time and the verifier's strategy can be implemented in almost-linear-time.
We present direct constructions of doubly-efficient interactive proof systems for problems in P that are believed to have relatively high complexity. Specifically, such constructions are presented for t-CLIQUE and t-SUM. In addition, we present a generic construction of such proof systems for a natural class that contains both problems and is in NC (and also in SC). The proof systems presented by us are significantly simpler than the proof systems presented by Goldwasser, Kalai and Rothblum (JACM, 2015), let alone those presented by Reingold, Rothblum, and Rothblum (STOC, 2016), and can be implemented using a smaller number of rounds.

Oded Goldreich and Guy N. Rothblum. Simple Doubly-Efficient Interactive Proof Systems for Locally-Characterizable Sets. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 18:1-18:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{goldreich_et_al:LIPIcs.ITCS.2018.18, author = {Goldreich, Oded and Rothblum, Guy N.}, title = {{Simple Doubly-Efficient Interactive Proof Systems for Locally-Characterizable Sets}}, booktitle = {9th Innovations in Theoretical Computer Science Conference (ITCS 2018)}, pages = {18:1--18:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-060-6}, ISSN = {1868-8969}, year = {2018}, volume = {94}, editor = {Karlin, Anna R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.18}, URN = {urn:nbn:de:0030-drops-83279}, doi = {10.4230/LIPIcs.ITCS.2018.18}, annote = {Keywords: Interactive proofs} }

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