1,720,957 research outputs found
The non-hardness of approximating circuit size
No full textThe Minimum Circuit Size Problem (MCSP) has been the focus of intense study recently; MCSP is hard for SZK under rather powerful reductions, and is provably not hard under “local” reductions computable in TIME(n^0.49). The question of whether MCSP is NP-hard (or indeed, hard even for small subclasses of P) under some of the more familiar notions of reducibility (such as many-one or Turing reductions computable in polynomial time or in AC0) is closely related to many of the longstanding open questions in complexity theory.
All prior hardness results for MCSP hold also for computing somewhat weak approximations to the circuit complexity of a function. Some of these results were proved by exploiting a connection to a notion of time-bounded Kolmogorov complexity (KT) and the corresponding decision problem (MKTP). More recently, a new approach for proving improved hardness results for MKTP was developed, but this approach establishes only hardness of extremely good approximations of the form 1+o(1), and these improved hardness results are not yet known to hold for MCSP. In particular, it is known that MKTP is hard for the complexity class DET under nonuniform AC0 many-one reductions, implying MKTP is not in AC0[p] for any prime p. It was still open if similar circuit lower bounds hold for MCSP. One possible avenue for proving a similar hardness result for MCSP would be to improve the hardness
of approximation for MKTP beyond 1 + o(1) to omega(1), as KT-complexity and circuit size are
polynomially-related. In this paper, we show that this approach cannot succeed.
More specifically, we prove that PARITY does not reduce to the problem of computing superlinear approximations to KT-complexity or circuit size via AC0-Turing reductions that make O(1) queries. This is significant, since approximating any set in P/poly AC0-reduces to just one query of a much worse approximation of circuit size or KT-complexity. For weaker approximations, we also prove non-hardness under more powerful reductions. Our non-hardness results are unconditional, in contrast to conditional results presented in [7] (for more powerful reductions, but for much worse approximations). This highlights obstacles that would have to be overcome by any proof that MKTP or MCSP is hard for NP under AC0 reductions. It may also be a step toward confirming a conjecture of Murray and Williams, that MCSP is not NP-complete under logtime-uniform AC0 many-one reductions.Peer reviewe
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Average-Case Hardness of NP and PH from Worst-Case Fine-Grained Assumptions
Get PDFWhat is a minimal worst-case complexity assumption that implies non-trivial average-case hardness of NP or PH? This question is well motivated by the theory of fine-grained average-case complexity and fine-grained cryptography. In this paper, we show that several standard worst-case complexity assumptions are sufficient to imply non-trivial average-case hardness of NP or PH:
- NTIME[n] cannot be solved in quasi-linear time on average if UP ̸ ⊆ DTIME[2^{Õ(√n)}].
- Σ₂TIME[n] cannot be solved in quasi-linear time on average if Σ_kSAT cannot be solved in time 2^{Õ(√n)} for some constant k. Previously, it was not known if even average-case hardness of Σ₃SAT implies the average-case hardness of Σ₂TIME[n].
- Under the Exponential-Time Hypothesis (ETH), there is no average-case n^{1+ε}-time algorithm for NTIME[n] whose running time can be estimated in time n^{1+ε} for some constant ε > 0.
Our results are given by generalizing the non-black-box worst-case-to-average-case connections presented by Hirahara (STOC 2021) to the settings of fine-grained complexity. To do so, we construct quite efficient complexity-theoretic pseudorandom generators under the assumption that the nondeterministic linear time is easy on average, which may be of independent interest
The Non-hardness of Approximating Circuit Size
No full textAbstract
The Minimum Circuit Size Problem (MCSP) has been the focus of intense study recently; MCSP is hard for SZK under rather powerful reductions (Allender and Das Inf. Comput. 256, 2–8, 2017), and is provably not hard under “local” reductions computable in TIME(n0.49) (Murray and Williams Theory Comput. 13(1), 1–22, 2017). The question of whether MCSP is NP-hard (or indeed, hard even for small subclasses of P) under some of the more familiar notions of reducibility (such as many-one or Turing reductions computable in polynomial time or in AC0) is closely related to many of the longstanding open questions in complexity theory (Allender and Hirahara ACM Trans. Comput. Theory 11(4), 27:1–27:27, 2019; Allender et al. Comput. Complex. 26(2), 469–496, 2017; Hirahara and Santhanam 2017; Hirahara and Watanabe 2016; Hitchcock and Pavan 2015; Impagliazzo et al. 2018; Murray and Williams Theory Comput. 13(1), 1–22, 2017). All prior hardness results for MCSP hold also for computing somewhat weak approximations to the circuit complexity of a function (Allender et al. SIAM J. Comput. 35(6), 1467–1493, 2006; Allender and Das Inf. Comput. 256, 2–8, 2017; Allender et al. J. Comput. Syst. Sci. 77(1), 14–40, 2011; Hirahara and Santhanam 2017; Kabanets and Cai 2000; Rudow Inf. Process. Lett. 128, 1–4, 2017) (Subsequent to our work, a new hardness result has been announced (Ilango 2020) that relies on more exact size computations). Some of these results were proved by exploiting a connection to a notion of time-bounded Kolmogorov complexity (KT) and the corresponding decision problem (MKTP). More recently, a new approach for proving improved hardness results for MKTP was developed (Allender et al. SIAM J. Comput. 47(4), 1339–1372, 2018; Allender and Hirahara ACM Trans. Comput. Theory 11(4), 27:1–27:27, 2019), but this approach establishes only hardness of extremely good approximations of the form 1 + o(1), and these improved hardness results are not yet known to hold for MCSP. In particular, it is known that MKTP is hard for the complexity class DET under nonuniform
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reductions, implying MKTP is not in AC0[p] for any prime p (Allender and Hirahara ACM Trans. Comput. Theory 11(4), 27:1–27:27, 2019). It was still open if similar circuit lower bounds hold for MCSP (But see Golovnev et al. 2019; Ilango 2020). One possible avenue for proving a similar hardness result for MCSP would be to improve the hardness of approximation for MKTP beyond 1 + o(1) to ω(1), as KT-complexity and circuit size are polynomially-related. In this paper, we show that this approach cannot succeed. More specifically, we prove that PARITY does not reduce to the problem of computing superlinear approximations to KT-complexity or circuit size via AC0-Turing reductions that make O(1) queries. This is significant, since approximating any set in P/poly AC0-reduces to just one query of a much worse approximation of circuit size or KT-complexity (Oliveira and Santhanam 2017). For weaker approximations, we also prove non-hardness under more powerful reductions. Our non-hardness results are unconditional, in contrast to conditional results presented in Allender and Hirahara (ACM Trans. Comput. Theory 11(4), 27:1–27:27, 2019) (for more powerful reductions, but for much worse approximations). This highlights obstacles that would have to be overcome by any proof that MKTP or MCSP is hard for NP under AC0 reductions. It may also be a step toward confirming a conjecture of Murray and Williams, that MCSP is not NP-complete under logtime-uniform
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Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
Memory Checking Requires Logarithmic Overhead
No full textWe study the complexity of memory checkers with computational security and prove the first general tight lower bound. Memory checkers, first introduced over 30 years ago by Blum, Evans, Gemmel, Kannan, and Naor (FOCS '91, Algorithmica '94), allow a user to store and maintain a large memory on a remote and unreliable server by using small trusted local storage. The user can issue instructions to the server and after every instruction, obtain either the correct value or a failure (but not an incorrect answer) with high probability. The main complexity measure of interest is the size of the local storage and the number of queries the memory checker makes upon every logical instruction. The most efficient known construction has query complexity and local space proportional to a computational security parameter, assuming one-way functions, where is the logical memory size. Dwork, Naor, Rothblum, and Vaikuntanathan (TCC '09) showed that for a restricted class of ``deterministic and non-adaptive' memory checkers, this construction is optimal, up to constant factors. However, going beyond the small class of deterministic and non-adaptive constructions has remained a major open problem. In this work, we fully resolve the complexity of memory checkers by showing that \emph{any} construction with local space and query complexity must satisfy This implies, as a special case, that in any scheme, assuming that for . The bound applies to any scheme with computational security, completeness , and inverse polynomial in soundness (all of which make our lower bound only stronger). We further extend the lower bound to schemes where the read complexity and write complexity differ. For instance, we show the tight bound that if and for , then . This is the first lower bound, for any non-trivial class of constructions, showing a read-write query complexity trade-off. Our proof is via a delicate compression argument showing that a ``too good to be true' memory checker can be used to compress random bits of information. We draw inspiration from tools recently developed for lower bounds for relaxed locally decodable codes. However, our proof itself significantly departs from these works, necessitated by the differences between settings
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