25 Search Results for "Ren, Michael"

Document
DOI: 10.4230/LIPIcs.CCC.2024.1
A Technique for Hardness Amplification Against AC⁰

Authors: William M. Hoza

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
We study hardness amplification in the context of two well-known "moderate" average-case hardness results for AC⁰ circuits. First, we investigate the extent to which AC⁰ circuits of depth d can approximate AC⁰ circuits of some larger depth d + k. The case k = 1 is resolved by Håstad, Rossman, Servedio, and Tan’s celebrated average-case depth hierarchy theorem (JACM 2017). Our contribution is a significantly stronger correlation bound when k ≥ 3. Specifically, we show that there exists a linear-size AC⁰_{d + k} circuit h : {0, 1}ⁿ → {0, 1} such that for every AC⁰_d circuit g, either g has size exp(n^{Ω(1/d)}), or else g agrees with h on at most a (1/2 + ε)-fraction of inputs where ε = exp(-(1/d) ⋅ Ω(log n)^{k-1}). For comparison, Håstad, Rossman, Servedio, and Tan’s result has ε = n^{-Θ(1/d)}. Second, we consider the majority function. It is well known that the majority function is moderately hard for AC⁰ circuits (and stronger classes). Our contribution is a stronger correlation bound for the XOR of t copies of the n-bit majority function, denoted MAJ_n^{⊕ t}. We show that if g is an AC⁰_d circuit of size S, then g agrees with MAJ_n^{⊕ t} on at most a (1/2 + ε)-fraction of inputs, where ε = (O(log S)^{d - 1} / √n)^t. To prove these results, we develop a hardness amplification technique that is tailored to a specific type of circuit lower bound proof. In particular, one way to show that a function h is moderately hard for AC⁰ circuits is to (a) design some distribution over random restrictions or random projections, (b) show that AC⁰ circuits simplify to shallow decision trees under these restrictions/projections, and finally (c) show that after applying the restriction/projection, h is moderately hard for shallow decision trees with respect to an appropriate distribution. We show that (roughly speaking) if h can be proven to be moderately hard by a proof with that structure, then XORing multiple copies of h amplifies its hardness. Our analysis involves a new kind of XOR lemma for decision trees, which might be of independent interest.
Cite as

William M. Hoza. A Technique for Hardness Amplification Against AC⁰. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hoza:LIPIcs.CCC.2024.1,
  author =	{Hoza, William M.},
  title =	{{A Technique for Hardness Amplification Against AC⁰}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{1:1--1:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.1},
  URN =		{urn:nbn:de:0030-drops-203977},
  doi =		{10.4230/LIPIcs.CCC.2024.1},
  annote =	{Keywords: Bounded-depth circuits, average-case lower bounds, hardness amplification, XOR lemmas}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.27
Baby PIH: Parameterized Inapproximability of Min CSP

Authors: Venkatesan Guruswami, Xuandi Ren, and Sai Sandeep

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
The Parameterized Inapproximability Hypothesis (PIH) is the analog of the PCP theorem in the world of parameterized complexity. It asserts that no FPT algorithm can distinguish a satisfiable 2CSP instance from one which is only (1-ε)-satisfiable (where the parameter is the number of variables) for some constant 0 < ε < 1. We consider a minimization version of CSPs (Min-CSP), where one may assign r values to each variable, and the goal is to ensure that every constraint is satisfied by some choice among the r × r pairs of values assigned to its variables (call such a CSP instance r-list-satisfiable). We prove the following strong parameterized inapproximability for Min CSP: For every r ≥ 1, it is W[1]-hard to tell if a 2CSP instance is satisfiable or is not even r-list-satisfiable. We refer to this statement as "Baby PIH", following the recently proved Baby PCP Theorem (Barto and Kozik, 2021). Our proof adapts the combinatorial arguments underlying the Baby PCP theorem, overcoming some basic obstacles that arise in the parameterized setting. Furthermore, our reduction runs in time polynomially bounded in both the number of variables and the alphabet size, and thus implies the Baby PCP theorem as well.
Cite as

Venkatesan Guruswami, Xuandi Ren, and Sai Sandeep. Baby PIH: Parameterized Inapproximability of Min CSP. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 27:1-27:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{guruswami_et_al:LIPIcs.CCC.2024.27,
  author =	{Guruswami, Venkatesan and Ren, Xuandi and Sandeep, Sai},
  title =	{{Baby PIH: Parameterized Inapproximability of Min CSP}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{27:1--27:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.27},
  URN =		{urn:nbn:de:0030-drops-204237},
  doi =		{10.4230/LIPIcs.CCC.2024.27},
  annote =	{Keywords: Parameterized Inapproximability Hypothesis, Constraint Satisfaction Problems}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.29
Exact Search-To-Decision Reductions for Time-Bounded Kolmogorov Complexity

Authors: Shuichi Hirahara, Valentine Kabanets, Zhenjian Lu, and Igor C. Oliveira

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
A search-to-decision reduction is a procedure that allows one to find a solution to a problem from the mere ability to decide when a solution exists. The existence of a search-to-decision reduction for time-bounded Kolmogorov complexity, i.e., the problem of checking if a string x can be generated by a t-time bounded program of description length s, is a long-standing open problem that dates back to the 1960s. In this work, we obtain new average-case and worst-case search-to-decision reductions for the complexity measure 𝖪^t and its randomized analogue rK^t: 1) (Conditional Errorless and Error-Prone Reductions for 𝖪^t) Under the assumption that 𝖤 requires exponential size circuits, we design polynomial-time average-case search-to-decision reductions for 𝖪^t in both errorless and error-prone settings. In fact, under the easiness of deciding 𝖪^t under the uniform distribution, we obtain a search algorithm for any given polynomial-time samplable distribution. In the error-prone reduction, the search algorithm works in the more general setting of conditional 𝖪^t complexity, i.e., it finds a minimum length t-time bound program for generating x given a string y. 2) (Unconditional Errorless Reduction for rK^t) We obtain an unconditional polynomial-time average-case search-to-decision reduction for rK^t in the errorless setting. Similarly to the results described above, we obtain a search algorithm for each polynomial-time samplable distribution, assuming the existence of a decision algorithm under the uniform distribution. To our knowledge, this is the first unconditional sub-exponential time search-to-decision reduction among the measures 𝖪^t and rK^t that works with respect to any given polynomial-time samplable distribution. 3) (Worst-Case to Average-Case Reductions) Under the errorless average-case easiness of deciding rK^t, we design a worst-case search algorithm running in time 2^O(n/log n) that produces a minimum length randomized t-time program for every input string x ∈ {0,1}ⁿ, with the caveat that it only succeeds on some explicitly computed sub-exponential time bound t ≤ 2^{n^ε} that depends on x. A similar result holds for 𝖪^t, under the assumption that 𝖤 requires exponential size circuits. In these results, the corresponding search problem is solved exactly, i.e., a successful run of the search algorithm outputs a t-time bounded program for x of minimum length, as opposed to an approximately optimal program of slightly larger description length or running time.
Cite as

Shuichi Hirahara, Valentine Kabanets, Zhenjian Lu, and Igor C. Oliveira. Exact Search-To-Decision Reductions for Time-Bounded Kolmogorov Complexity. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 29:1-29:56, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{hirahara_et_al:LIPIcs.CCC.2024.29,
  author =	{Hirahara, Shuichi and Kabanets, Valentine and Lu, Zhenjian and Oliveira, Igor C.},
  title =	{{Exact Search-To-Decision Reductions for Time-Bounded Kolmogorov Complexity}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{29:1--29:56},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.29},
  URN =		{urn:nbn:de:0030-drops-204256},
  doi =		{10.4230/LIPIcs.CCC.2024.29},
  annote =	{Keywords: average-case complexity, Kolmogorov complexity, search-to-decision reductions}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.36
Gap MCSP Is Not (Levin) NP-Complete in Obfustopia

Authors: Noam Mazor and Rafael Pass

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
We demonstrate that under believable cryptographic hardness assumptions, Gap versions of standard meta-complexity problems, such as the Minimum Circuit Size Problem (MCSP) and the Minimum Time-Bounded Kolmogorov Complexity problem (MKTP) are not NP-complete w.r.t. Levin (i.e., witness-preserving many-to-one) reductions. In more detail: - Assuming the existence of indistinguishability obfuscation, and subexponentially-secure one-way functions, an appropriate Gap version of MCSP is not NP-complete under randomized Levin-reductions. - Assuming the existence of subexponentially-secure indistinguishability obfuscation, subexponentially-secure one-way functions and injective PRGs, an appropriate Gap version of MKTP is not NP-complete under randomized Levin-reductions.
Cite as

Noam Mazor and Rafael Pass. Gap MCSP Is Not (Levin) NP-Complete in Obfustopia. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 36:1-36:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{mazor_et_al:LIPIcs.CCC.2024.36,
  author =	{Mazor, Noam and Pass, Rafael},
  title =	{{Gap MCSP Is Not (Levin) NP-Complete in Obfustopia}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{36:1--36:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.36},
  URN =		{urn:nbn:de:0030-drops-204322},
  doi =		{10.4230/LIPIcs.CCC.2024.36},
  annote =	{Keywords: Kolmogorov complexity, MCSP, Levin Reduction}
}
Document
DOI: 10.4230/LIPIcs.ECRTS.2024.1
JuMP2start: Time-Aware Stop-Start Technology for a Software-Defined Vehicle System

Authors: Anam Farrukh and Richard West

Published in: LIPIcs, Volume 298, 36th Euromicro Conference on Real-Time Systems (ECRTS 2024)

Abstract
Software-defined vehicle (SDV) systems replace traditional ECU architectures with software tasks running on centralized multicore processors in automotive-grade PCs. However, PC boot delays to cold-start an integrated vehicle management system (VMS) are problematic for time-critical functions, which must process sensor and actuator data within specific time bounds. To tackle this challenge, we present JuMP2start: a time-aware multicore stop-start approach for SDVs. JuMP2start leverages PC-class suspend-to-RAM techniques to capture a system snapshot when the vehicle is stopped. Upon restart, critical services are resumed-from-RAM within order of milliseconds compared to normal cold-start times. This work showcases how JuMP2start manages global suspension and resumption mechanisms for a state-of-the-art dual-domain vehicle management system comprising real-time OS (RTOS) and Linux SMP guests. JuMP2start models automotive tasks as continuable or restartable to ensure timing- and safety-critical function pipelines are reactively resumed with low latency, while discarding stale task state. Experiments with the VMS show that critical CAN traffic processing resumes within 500 milliseconds of waking the RTOS guest, and reaches steady-state throughput in under 7ms.
Cite as

Anam Farrukh and Richard West. JuMP2start: Time-Aware Stop-Start Technology for a Software-Defined Vehicle System. In 36th Euromicro Conference on Real-Time Systems (ECRTS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 298, pp. 1:1-1:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{farrukh_et_al:LIPIcs.ECRTS.2024.1,
  author =	{Farrukh, Anam and West, Richard},
  title =	{{JuMP2start: Time-Aware Stop-Start Technology for a Software-Defined Vehicle System}},
  booktitle =	{36th Euromicro Conference on Real-Time Systems (ECRTS 2024)},
  pages =	{1:1--1:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-324-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{298},
  editor =	{Pellizzoni, Rodolfo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECRTS.2024.1},
  URN =		{urn:nbn:de:0030-drops-203046},
  doi =		{10.4230/LIPIcs.ECRTS.2024.1},
  annote =	{Keywords: Time-aware stop-start, Real-time power management, Suspend-to-RAM, Partitioning hypervisor, Vehicle management system, Vehicle-OS, Software-defined vehicles (SDV)}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.15
List Update with Delays or Time Windows

Authors: Yossi Azar, Shahar Lewkowicz, and Danny Vainstein

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We address the problem of List Update, which is considered one of the fundamental problems in online algorithms and competitive analysis. In this context, we are presented with a list of elements and receive requests for these elements over time. Our objective is to fulfill these requests, incurring a cost proportional to their position in the list. Additionally, we can swap any two consecutive elements at a cost of 1. The renowned "Move to Front" algorithm, introduced by Sleator and Tarjan, immediately moves any requested element to the front of the list. They demonstrated that this algorithm achieves a competitive ratio of 2. While this bound is impressive, the actual cost of the algorithm’s solution can be excessively high. For example, if we request the last half of the list, the resulting solution cost becomes quadratic in the list’s length. To address this issue, we consider a more generalized problem called List Update with Time Windows. In this variant, each request arrives with a specific deadline by which it must be served, rather than being served immediately. Moreover, we allow the algorithm to process multiple requests simultaneously, accessing the corresponding elements in a single pass. The cost incurred in this case is determined by the position of the furthest element accessed, leading to a significant reduction in the total solution cost. We introduce this problem to explore lower solution costs, but it necessitates the development of new algorithms. For instance, Move-to-Front fails when handling the simple scenario of requesting the last half of the list with overlapping time windows. In our work, we present a natural O(1) competitive algorithm for this problem. While the algorithm itself is intuitive, its analysis is intricate, requiring the use of a novel potential function. Additionally, we delve into a more general problem called List Update with Delays, where the fixed deadlines are replaced with arbitrary delay functions. In this case, the cost includes not only the access and swapping costs, but also penalties for the delays incurred until the requests are served. This problem encompasses a special case known as the prize collecting version, where a request may go unserved up to a given deadline, resulting in a specified penalty. For this more comprehensive problem, we establish an O(1) competitive algorithm. However, the algorithm for the delay version is more complex, and its analysis involves significantly more intricate considerations.
Cite as

Yossi Azar, Shahar Lewkowicz, and Danny Vainstein. List Update with Delays or Time Windows. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 15:1-15:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{azar_et_al:LIPIcs.ICALP.2024.15,
  author =	{Azar, Yossi and Lewkowicz, Shahar and Vainstein, Danny},
  title =	{{List Update with Delays or Time Windows}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{15:1--15:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.15},
  URN =		{urn:nbn:de:0030-drops-201583},
  doi =		{10.4230/LIPIcs.ICALP.2024.15},
  annote =	{Keywords: Online, List Update, Delay, Time Window, Deadline}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.107
Improved Lower Bounds for Approximating Parameterized Nearest Codeword and Related Problems Under ETH

Authors: Shuangle Li, Bingkai Lin, and Yuwei Liu

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this paper we present a new gap-creating randomized self-reduction for the parameterized Maximum Likelihood Decoding problem over 𝔽_p (k-MLD_p). The reduction takes a k-MLD_p instance with k⋅ n d-dimensional vectors as input, runs in O(d2^{O(k)}n^{1.01}) time for some computable function f, outputs a (3/2-ε)-Gap-k'-MLD_p instance for any ε > 0, where k' = O(k²log k). Using this reduction, we show that assuming the randomized Exponential Time Hypothesis (ETH), no algorithms can approximate k-MLD_p (and therefore its dual problem k-NCP_p) within factor (3/2-ε) in f(k)⋅ n^{o(√{k/log k})} time for any ε > 0. We then use reduction by Bhattacharyya, Ghoshal, Karthik and Manurangsi (ICALP 2018) to amplify the (3/2-ε)-gap to any constant. As a result, we show that assuming ETH, no algorithms can approximate k-NCP_p and k-MDP_p within γ-factor in f(k)⋅ n^{o(k^{ε_γ})} time for some constant ε_γ > 0. Combining with the gap-preserving reduction by Bennett, Cheraghchi, Guruswami and Ribeiro (STOC 2023), we also obtain similar lower bounds for k-MDP_p, k-CVP_p and k-SVP_p. These results improve upon the previous f(k)⋅ n^{Ω(poly log k)} lower bounds for these problems under ETH using reductions by Bhattacharyya et al. (J.ACM 2021) and Bennett et al. (STOC 2023).
Cite as

Shuangle Li, Bingkai Lin, and Yuwei Liu. Improved Lower Bounds for Approximating Parameterized Nearest Codeword and Related Problems Under ETH. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 107:1-107:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{li_et_al:LIPIcs.ICALP.2024.107,
  author =	{Li, Shuangle and Lin, Bingkai and Liu, Yuwei},
  title =	{{Improved Lower Bounds for Approximating Parameterized Nearest Codeword and Related Problems Under ETH}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{107:1--107:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.107},
  URN =		{urn:nbn:de:0030-drops-202500},
  doi =		{10.4230/LIPIcs.ICALP.2024.107},
  annote =	{Keywords: Nearest Codeword Problem, Hardness of Approximations, Fine-grained Complexity, Parameterized Complexity, Minimum Distance Problem, Shortest Vector Problem}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.110
Impagliazzo’s Worlds Through the Lens of Conditional Kolmogorov Complexity

Authors: Zhenjian Lu and Rahul Santhanam

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We develop new characterizations of Impagliazzo’s worlds Algorithmica, Heuristica and Pessiland by the intractability of conditional Kolmogorov complexity 𝖪 and conditional probabilistic time-bounded Kolmogorov complexity pK^t. In our first set of results, we show that NP ⊆ BPP iff pK^t(x ∣ y) can be computed efficiently in the worst case when t is sublinear in |x| + |y|; DistNP ⊆ HeurBPP iff pK^t(x ∣ y) can be computed efficiently over all polynomial-time samplable distributions when t is sublinear in |x| + |y|; and infinitely-often one-way functions fail to exist iff pK^t(x ∣ y) can be computed efficiently over all polynomial-time samplable distributions for t a sufficiently large polynomial in |x| + |y|. These results characterize Impagliazzo’s worlds Algorithmica, Heuristica and Pessiland purely in terms of the tractability of conditional pK^t. Notably, the results imply that Pessiland fails to exist iff the average-case intractability of conditional pK^t is insensitive to the difference between sublinear and polynomially bounded t. As a corollary, while we prove conditional pK^t to be NP-hard for sublinear t, showing NP-hardness for large enough polynomially bounded t would eliminate Pessiland as a possible world of average-case complexity. In our second set of results, we characterize Impagliazzo’s worlds Algorithmica, Heuristica and Pessiland by the distributional tractability of a natural problem, i.e., approximating the conditional Kolmogorov complexity, that is provably intractable in the worst case. We show that NP ⊆ BPP iff conditional Kolmogorov complexity can be approximated in the semi-worst case; and DistNP ⊆ HeurBPP iff conditional Kolmogorov complexity can be approximated on average over all independent polynomial-time samplable distributions. It follows from a result by Ilango, Ren, and Santhanam (STOC 2022) that infinitely-often one-way functions fail to exist iff conditional Kolmogorov complexity can be approximated on average over all polynomial-time samplable distributions. Together, these results yield the claimed characterizations. Our techniques, combined with previous work, also yield a characterization of auxiliary-input one-way functions and equivalences between different average-case tractability assumptions for conditional Kolmogorov complexity and its variants. Our results suggest that novel average-case tractability assumptions such as tractability in the semi-worst case and over independent polynomial-time samplable distributions might be worthy of further study.
Cite as

Zhenjian Lu and Rahul Santhanam. Impagliazzo’s Worlds Through the Lens of Conditional Kolmogorov Complexity. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 110:1-110:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{lu_et_al:LIPIcs.ICALP.2024.110,
  author =	{Lu, Zhenjian and Santhanam, Rahul},
  title =	{{Impagliazzo’s Worlds Through the Lens of Conditional Kolmogorov Complexity}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{110:1--110:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.110},
  URN =		{urn:nbn:de:0030-drops-202538},
  doi =		{10.4230/LIPIcs.ICALP.2024.110},
  annote =	{Keywords: meta-complexity, Kolmogorov complexity, one-way functions, average-case complexity}
}
Document
Position
DOI: 10.4230/TGDK.2.1.2
Grounding Stream Reasoning Research

Authors: Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer

Published in: TGDK, Volume 2, Issue 1 (2024): Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge, Volume 2, Issue 1

Abstract
In the last decade, there has been a growing interest in applying AI technologies to implement complex data analytics over data streams. To this end, researchers in various fields have been organising a yearly event called the "Stream Reasoning Workshop" to share perspectives, challenges, and experiences around this topic. In this paper, the previous organisers of the workshops and other community members provide a summary of the main research results that have been discussed during the first six editions of the event. These results can be categorised into four main research areas: The first is concerned with the technological challenges related to handling large data streams. The second area aims at adapting and extending existing semantic technologies to data streams. The third and fourth areas focus on how to implement reasoning techniques, either considering deductive or inductive techniques, to extract new and valuable knowledge from the data in the stream. This summary is written not only to provide a crystallisation of the field, but also to point out distinctive traits of the stream reasoning community. Moreover, it also provides a foundation for future research by enumerating a list of use cases and open challenges, to stimulate others to join this exciting research area.
Cite as

Pieter Bonte, Jean-Paul Calbimonte, Daniel de Leng, Daniele Dell'Aglio, Emanuele Della Valle, Thomas Eiter, Federico Giannini, Fredrik Heintz, Konstantin Schekotihin, Danh Le-Phuoc, Alessandra Mileo, Patrik Schneider, Riccardo Tommasini, Jacopo Urbani, and Giacomo Ziffer. Grounding Stream Reasoning Research. In Special Issue on Trends in Graph Data and Knowledge - Part 2. Transactions on Graph Data and Knowledge (TGDK), Volume 2, Issue 1, pp. 2:1-2:47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{bonte_et_al:TGDK.2.1.2,
  author =	{Bonte, Pieter and Calbimonte, Jean-Paul and de Leng, Daniel and Dell'Aglio, Daniele and Della Valle, Emanuele and Eiter, Thomas and Giannini, Federico and Heintz, Fredrik and Schekotihin, Konstantin and Le-Phuoc, Danh and Mileo, Alessandra and Schneider, Patrik and Tommasini, Riccardo and Urbani, Jacopo and Ziffer, Giacomo},
  title =	{{Grounding Stream Reasoning Research}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{2:1--2:47},
  ISSN =	{2942-7517},
  year =	{2024},
  volume =	{2},
  number =	{1},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.2.1.2},
  URN =		{urn:nbn:de:0030-drops-198597},
  doi =		{10.4230/TGDK.2.1.2},
  annote =	{Keywords: Stream Reasoning, Stream Processing, RDF streams, Streaming Linked Data, Continuous query processing, Temporal Logics, High-performance computing, Databases}
}
Document
DOI: 10.4230/DagRep.13.8.1
Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)

Authors: George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman

Published in: Dagstuhl Reports, Volume 13, Issue 8 (2024)

Abstract
This report documents the program and the outcomes of Dagstuhl Seminar 23331 "Recent Trends in Graph Decomposition", which took place from 13. August to 18. August, 2023. The seminar brought together 33 experts from academia and industry to discuss graph decomposition, a pivotal technique for handling massive graphs in applications such as social networks and scientific simulations. The seminar addressed the challenges posed by contemporary hardware designs, the potential of deep neural networks and reinforcement learning in developing heuristics, the unique optimization requirements of large sparse data, and the need for scalable algorithms suitable for emerging architectures. Through presentations, discussions, and collaborative sessions, the event fostered an exchange of innovative ideas, leading to the creation of community notes highlighting key open problems in the field.
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George Karypis, Christian Schulz, Darren Strash, Deepak Ajwani, Rob H. Bisseling, Katrin Casel, Ümit V. Çatalyürek, Cédric Chevalier, Florian Chudigiewitsch, Marcelo Fonseca Faraj, Michael Fellows, Lars Gottesbüren, Tobias Heuer, Kamer Kaya, Jakub Lacki, Johannes Langguth, Xiaoye Sherry Li, Ruben Mayer, Johannes Meintrup, Yosuke Mizutani, François Pellegrini, Fabrizio Petrini, Frances Rosamond, Ilya Safro, Sebastian Schlag, Roohani Sharma, Blair D. Sullivan, Bora Uçar, and Albert-Jan Yzelman. Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331). In Dagstuhl Reports, Volume 13, Issue 8, pp. 1-45, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@Article{karypis_et_al:DagRep.13.8.1,
  author =	{Karypis, George and Schulz, Christian and Strash, Darren and Ajwani, Deepak and Bisseling, Rob H. and Casel, Katrin and \c{C}ataly\"{u}rek, \"{U}mit V. and Chevalier, C\'{e}dric and Chudigiewitsch, Florian and Faraj, Marcelo Fonseca and Fellows, Michael and Gottesb\"{u}ren, Lars and Heuer, Tobias and Kaya, Kamer and Lacki, Jakub and Langguth, Johannes and Li, Xiaoye Sherry and Mayer, Ruben and Meintrup, Johannes and Mizutani, Yosuke and Pellegrini, Fran\c{c}ois and Petrini, Fabrizio and Rosamond, Frances and Safro, Ilya and Schlag, Sebastian and Sharma, Roohani and Sullivan, Blair D. and U\c{c}ar, Bora and Yzelman, Albert-Jan},
  title =	{{Recent Trends in Graph Decomposition (Dagstuhl Seminar 23331)}},
  pages =	{1--45},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2024},
  volume =	{13},
  number =	{8},
  editor =	{Karypis, George and Schulz, Christian and Strash, Darren},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.13.8.1},
  URN =		{urn:nbn:de:0030-drops-198114},
  doi =		{10.4230/DagRep.13.8.1},
  annote =	{Keywords: combinatorial optimization, experimental algorithmics, parallel algorithms}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ITP.2023.2
Interactive and Automated Proofs in Modal Separation Logic (Invited Talk)

Authors: Robbert Krebbers

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract
In program verification, it is common to embed a high-level object logic into the meta logic of a proof assistant to hide low-level aspects of the verification. To verify imperative and concurrent programs, separation logic hides explicit reasoning about heaps and pointer disjointness. To verify programs with cyclic features such as modules or higher-order state, modal logic provides modalities to hide explicit reasoning about step-indices that are used to stratify recursion. The meta logic of proof assistants such as Coq is well suited to embed high-level object logics and prove their soundness. However, proof assistants such as Coq do not have native infrastructure to facilitate proofs in embedded logics - their proof contexts and built-in tactics for interactive and automated proofs are tailored to the connectives of the meta logic, and do not extend to those of the object logic. This results in proofs that are at a too low level of abstraction because they are cluttered with bookkeeping code related to manipulating the object logic. In this talk I will describe our work in the Iris project to address this problem - first for interactive proofs, and then for semi-automated proofs. The Iris Proof Mode provides high-level tactics for interactive proofs in higher-order concurrent separation logic with modalities. Recent work on RefinedC and Diaframe have built on top of the Iris Proof Mode to obtain proof automation for low-level C programs and fine-grained concurrent programs.
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Robbert Krebbers. Interactive and Automated Proofs in Modal Separation Logic (Invited Talk). In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{krebbers:LIPIcs.ITP.2023.2,
  author =	{Krebbers, Robbert},
  title =	{{Interactive and Automated Proofs in Modal Separation Logic}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.2},
  URN =		{urn:nbn:de:0030-drops-183770},
  doi =		{10.4230/LIPIcs.ITP.2023.2},
  annote =	{Keywords: Program Verification, Separation Logic, Step-Indexing, Modal Logic, Interactive Theorem Proving, Proof Automation, Iris, Coq}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.6
An Elementary Formal Proof of the Group Law on Weierstrass Elliptic Curves in Any Characteristic

Authors: David Kurniadi Angdinata and Junyan Xu

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract
Elliptic curves are fundamental objects in number theory and algebraic geometry, whose points over a field form an abelian group under a geometric addition law. Any elliptic curve over a field admits a Weierstrass model, but prior formal proofs that the addition law is associative in this model involve either advanced algebraic geometry or tedious computation, especially in characteristic two. We formalise in the Lean theorem prover, the type of nonsingular points of a Weierstrass curve over a field of any characteristic and a purely algebraic proof that it forms an abelian group.
Cite as

David Kurniadi Angdinata and Junyan Xu. An Elementary Formal Proof of the Group Law on Weierstrass Elliptic Curves in Any Characteristic. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{angdinata_et_al:LIPIcs.ITP.2023.6,
  author =	{Angdinata, David Kurniadi and Xu, Junyan},
  title =	{{An Elementary Formal Proof of the Group Law on Weierstrass Elliptic Curves in Any Characteristic}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.6},
  URN =		{urn:nbn:de:0030-drops-183817},
  doi =		{10.4230/LIPIcs.ITP.2023.6},
  annote =	{Keywords: formal math, algebraic geometry, elliptic curve, group law, Lean, mathlib}
}
Document
DOI: 10.4230/LIPIcs.ITP.2023.33
Dependently Sorted Theorem Proving for Mathematical Foundations

Authors: Yiming Xu and Michael Norrish

Published in: LIPIcs, Volume 268, 14th International Conference on Interactive Theorem Proving (ITP 2023)

Abstract
We describe a new meta-logical system for mechanising foundations of mathematics. Using dependent sorts and first order logic, our system (implemented as an LCF-style theorem-prover) improves on the state-of-the-art by providing efficient type-checking, convenient automatic rewriting and interactive proof support. We assess our implementation by axiomatising Lawvere’s Elementary Theory of the Category of Sets (ETCS) [F. William Lawvere, 1964], and Shulman’s Sets, Elements and Relations (SEAR) [Michael Shulman, 2022]. We then demonstrate our system’s ability to perform some basic mathematical constructions such as quotienting, induction and coinduction by constructing integers, lists and colists. We also compare with some existing work on modal model theory done in HOL4 [Yiming Xu and Michael Norrish, 2020]. Using the analogue of type-quantification, we are able to prove a theorem that this earlier work could not. Finally, we show that SEAR can construct sets that are larger than any finite iteration of the power set operation. This shows that SEAR, unlike HOL, can construct sets beyond V_{ω+ω}.
Cite as

Yiming Xu and Michael Norrish. Dependently Sorted Theorem Proving for Mathematical Foundations. In 14th International Conference on Interactive Theorem Proving (ITP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 268, pp. 33:1-33:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{xu_et_al:LIPIcs.ITP.2023.33,
  author =	{Xu, Yiming and Norrish, Michael},
  title =	{{Dependently Sorted Theorem Proving for Mathematical Foundations}},
  booktitle =	{14th International Conference on Interactive Theorem Proving (ITP 2023)},
  pages =	{33:1--33:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-284-6},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{268},
  editor =	{Naumowicz, Adam and Thiemann, Ren\'{e}},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2023.33},
  URN =		{urn:nbn:de:0030-drops-184085},
  doi =		{10.4230/LIPIcs.ITP.2023.33},
  annote =	{Keywords: first order logic, sorts, structural set theory, mechanised mathematics, foundation of mathematics, category theory}
}
Document
DOI: 10.4230/LIPIcs.SEA.2022.13
A Branch-And-Bound Algorithm for Cluster Editing

Authors: Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm

Published in: LIPIcs, Volume 233, 20th International Symposium on Experimental Algorithms (SEA 2022)

Abstract
The cluster editing problem asks to transform a given graph into a disjoint union of cliques by inserting and deleting as few edges as possible. We describe and evaluate an exact branch-and-bound algorithm for cluster editing. For this, we introduce new reduction rules and adapt existing ones. Moreover, we generalize a known packing technique to obtain lower bounds and experimentally show that it contributes significantly to the performance of the solver. Our experiments further evaluate the effectiveness of the different reduction rules and examine the effects of structural properties of the input graph on solver performance. Our solver won the exact track of the 2021 PACE challenge.
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Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. A Branch-And-Bound Algorithm for Cluster Editing. In 20th International Symposium on Experimental Algorithms (SEA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 233, pp. 13:1-13:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{blasius_et_al:LIPIcs.SEA.2022.13,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
  title =	{{A Branch-And-Bound Algorithm for Cluster Editing}},
  booktitle =	{20th International Symposium on Experimental Algorithms (SEA 2022)},
  pages =	{13:1--13:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-251-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{233},
  editor =	{Schulz, Christian and U\c{c}ar, Bora},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2022.13},
  URN =		{urn:nbn:de:0030-drops-165473},
  doi =		{10.4230/LIPIcs.SEA.2022.13},
  annote =	{Keywords: cluster editing}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2021.27
PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm

Authors: Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm

Published in: LIPIcs, Volume 214, 16th International Symposium on Parameterized and Exact Computation (IPEC 2021)

Abstract
The cluster editing problem is to transform an input graph into a cluster graph by performing a minimum number of edge editing operations. A cluster graph is a graph where each connected component is a clique. An edit operation can be either adding a new edge or removing an existing edge. In this write-up we outline the core techniques used in the exact cluster editing algorithm of the KaPoCE framework (contains also a heuristic solver), submitted to the exact track of the 2021 PACE challenge.
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Thomas Bläsius, Philipp Fischbeck, Lars Gottesbüren, Michael Hamann, Tobias Heuer, Jonas Spinner, Christopher Weyand, and Marcus Wilhelm. PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm. In 16th International Symposium on Parameterized and Exact Computation (IPEC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 214, pp. 27:1-27:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{blasius_et_al:LIPIcs.IPEC.2021.27,
  author =	{Bl\"{a}sius, Thomas and Fischbeck, Philipp and Gottesb\"{u}ren, Lars and Hamann, Michael and Heuer, Tobias and Spinner, Jonas and Weyand, Christopher and Wilhelm, Marcus},
  title =	{{PACE Solver Description: The KaPoCE Exact Cluster Editing Algorithm}},
  booktitle =	{16th International Symposium on Parameterized and Exact Computation (IPEC 2021)},
  pages =	{27:1--27:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-216-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{214},
  editor =	{Golovach, Petr A. and Zehavi, Meirav},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2021.27},
  URN =		{urn:nbn:de:0030-drops-154109},
  doi =		{10.4230/LIPIcs.IPEC.2021.27},
  annote =	{Keywords: cluster editing}
}
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