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**Published in:** LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Inspired by the classic problem of Boolean function monotonicity testing, we investigate the testability of other well-studied properties of combinatorial finite set systems, specifically intersecting families and union-closed families. A function f: {0,1}ⁿ → {0,1} is intersecting (respectively, union-closed) if its set of satisfying assignments corresponds to an intersecting family (respectively, a union-closed family) of subsets of [n].
Our main results are that - in sharp contrast with the property of being a monotone set system - the property of being an intersecting set system, and the property of being a union-closed set system, both turn out to be information-theoretically difficult to test. We show that:
- For ε ≥ Ω(1/√n), any non-adaptive two-sided ε-tester for intersectingness must make 2^{Ω(n^{1/4}/√{ε})} queries. We also give a 2^{Ω(√{n log(1/ε)})}-query lower bound for non-adaptive one-sided ε-testers for intersectingness.
- For ε ≥ 1/2^{Ω(n^{0.49})}, any non-adaptive two-sided ε-tester for union-closedness must make n^{Ω(log(1/ε))} queries.
Thus, neither intersectingness nor union-closedness shares the poly(n,1/ε)-query non-adaptive testability that is enjoyed by monotonicity.
To complement our lower bounds, we also give a simple poly(n^{√{nlog(1/ε)}},1/ε)-query, one-sided, non-adaptive algorithm for ε-testing each of these properties (intersectingness and union-closedness). We thus achieve nearly tight upper and lower bounds for two-sided testing of intersectingness when ε = Θ(1/√n), and for one-sided testing of intersectingness when ε = Θ(1).

Xi Chen, Anindya De, Yuhao Li, Shivam Nadimpalli, and Rocco A. Servedio. Testing Intersecting and Union-Closed Families. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 33:1-33:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2024.33, author = {Chen, Xi and De, Anindya and Li, Yuhao and Nadimpalli, Shivam and Servedio, Rocco A.}, title = {{Testing Intersecting and Union-Closed Families}}, booktitle = {15th Innovations in Theoretical Computer Science Conference (ITCS 2024)}, pages = {33:1--33:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-309-6}, ISSN = {1868-8969}, year = {2024}, volume = {287}, editor = {Guruswami, Venkatesan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.33}, URN = {urn:nbn:de:0030-drops-195610}, doi = {10.4230/LIPIcs.ITCS.2024.33}, annote = {Keywords: Sublinear algorithms, property testing, computational complexity, monotonicity, intersecting families, union-closed families} }

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RANDOM

**Published in:** LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

A major goal in the area of exact exponential algorithms is to give an algorithm for the (worst-case) n-input Subset Sum problem that runs in time 2^{(1/2 - c)n} for some constant c > 0. In this paper we give a Subset Sum algorithm with worst-case running time O(2^{n/2} ⋅ n^{-γ}) for a constant γ > 0.5023 in standard word RAM or circuit RAM models. To the best of our knowledge, this is the first improvement on the classical "meet-in-the-middle" algorithm for worst-case Subset Sum, due to Horowitz and Sahni, which can be implemented in time O(2^{n/2}) in these memory models [Horowitz and Sahni, 1974].
Our algorithm combines a number of different techniques, including the "representation method" introduced by Howgrave-Graham and Joux [Howgrave-Graham and Joux, 2010] and subsequent adaptations of the method in Austrin, Kaski, Koivisto, and Nederlof [Austrin et al., 2016], and Nederlof and Węgrzycki [Jesper Nederlof and Karol Wegrzycki, 2021], and "bit-packing" techniques used in the work of Baran, Demaine, and Pǎtraşcu [Baran et al., 2005] on subquadratic algorithms for 3SUM.

Xi Chen, Yaonan Jin, Tim Randolph, and Rocco A. Servedio. Subset Sum in Time 2^{n/2} / poly(n). In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 39:1-39:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.APPROX/RANDOM.2023.39, author = {Chen, Xi and Jin, Yaonan and Randolph, Tim and Servedio, Rocco A.}, title = {{Subset Sum in Time 2^\{n/2\} / poly(n)}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)}, pages = {39:1--39:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-296-9}, ISSN = {1868-8969}, year = {2023}, volume = {275}, editor = {Megow, Nicole and Smith, Adam}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2023.39}, URN = {urn:nbn:de:0030-drops-188641}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2023.39}, annote = {Keywords: Exact algorithms, subset sum, log shaving} }

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**Published in:** LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)

We study the problem of finding a Tarski fixed point over the k-dimensional grid [n]^k. We give a black-box reduction from the Tarski problem to the same problem with an additional promise that the input function has a unique fixed point. It implies that the Tarski problem and the unique Tarski problem have exactly the same query complexity. Our reduction is based on a novel notion of partial-information functions which we use to fool algorithms for the unique Tarski problem as if they were working on a monotone function with a unique fixed point.

Xi Chen, Yuhao Li, and Mihalis Yannakakis. Reducing Tarski to Unique Tarski (In the Black-Box Model). In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 21:1-21:23, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.CCC.2023.21, author = {Chen, Xi and Li, Yuhao and Yannakakis, Mihalis}, title = {{Reducing Tarski to Unique Tarski (In the Black-Box Model)}}, booktitle = {38th Computational Complexity Conference (CCC 2023)}, pages = {21:1--21:23}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-282-2}, ISSN = {1868-8969}, year = {2023}, volume = {264}, editor = {Ta-Shma, Amnon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.21}, URN = {urn:nbn:de:0030-drops-182919}, doi = {10.4230/LIPIcs.CCC.2023.21}, annote = {Keywords: Tarski fixed point, Query complexity, TFNP} }

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

In the trace reconstruction problem, an unknown source string x ∈ {0,1}ⁿ is transmitted through a probabilistic deletion channel which independently deletes each bit with some fixed probability δ and concatenates the surviving bits, resulting in a trace of x. The problem is to reconstruct x given access to independent traces. Trace reconstruction of arbitrary (worst-case) strings is a challenging problem, with the current state of the art for poly(n)-time algorithms being the 2004 algorithm of Batu et al. [T. Batu et al., 2004]. This algorithm can reconstruct an arbitrary source string x ∈ {0,1}ⁿ in poly(n) time provided that the deletion rate δ satisfies δ ≤ n^{-(1/2 + ε)} for some ε > 0.
In this work we improve on the result of [T. Batu et al., 2004] by giving a poly(n)-time algorithm for trace reconstruction for any deletion rate δ ≤ n^{-(1/3 + ε)}. Our algorithm works by alternating an alignment-based procedure, which we show effectively reconstructs portions of the source string that are not "highly repetitive", with a novel procedure that efficiently determines the length of highly repetitive subwords of the source string.

Xi Chen, Anindya De, Chin Ho Lee, Rocco A. Servedio, and Sandip Sinha. Polynomial-Time Trace Reconstruction in the Low Deletion Rate Regime. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 20:1-20:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2021.20, author = {Chen, Xi and De, Anindya and Lee, Chin Ho and Servedio, Rocco A. and Sinha, Sandip}, title = {{Polynomial-Time Trace Reconstruction in the Low Deletion Rate Regime}}, booktitle = {12th Innovations in Theoretical Computer Science Conference (ITCS 2021)}, pages = {20:1--20:20}, 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.2021.20}, URN = {urn:nbn:de:0030-drops-135595}, doi = {10.4230/LIPIcs.ITCS.2021.20}, annote = {Keywords: trace reconstruction} }

Document

RANDOM

**Published in:** LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

A number of recent works have considered the trace reconstruction problem, in which an unknown source string x in {0,1}^n is transmitted through a probabilistic channel which may randomly delete coordinates or insert random bits, resulting in a trace of x. The goal is to reconstruct the original string x from independent traces of x. While the asymptotically best algorithms known for worst-case strings use exp(O(n^{1/3})) traces [De et al., 2017; Fedor Nazarov and Yuval Peres, 2017], several highly efficient algorithms are known [Yuval Peres and Alex Zhai, 2017; Nina Holden et al., 2018] for the average-case version of the problem, in which the source string x is chosen uniformly at random from {0,1}^n. In this paper we consider a generalization of the above-described average-case trace reconstruction problem, which we call average-case population recovery in the presence of insertions and deletions. In this problem, rather than a single unknown source string there is an unknown distribution over s unknown source strings x^1,...,x^s in {0,1}^n, and each sample given to the algorithm is independently generated by drawing some x^i from this distribution and returning an independent trace of x^i. Building on the results of [Yuval Peres and Alex Zhai, 2017] and [Nina Holden et al., 2018], we give an efficient algorithm for the average-case population recovery problem in the presence of insertions and deletions. For any support size 1 <= s <= exp(Theta(n^{1/3})), for a 1-o(1) fraction of all s-element support sets {x^1,...,x^s} subset {0,1}^n, for every distribution D supported on {x^1,...,x^s}, our algorithm can efficiently recover D up to total variation distance at most epsilon with high probability, given access to independent traces of independent draws from D. The running time of our algorithm is poly(n,s,1/epsilon) and its sample complexity is poly (s,1/epsilon,exp(log^{1/3} n)). This polynomial dependence on the support size s is in sharp contrast with the worst-case version of the problem (when x^1,...,x^s may be any strings in {0,1}^n), in which the sample complexity of the most efficient known algorithm [Frank Ban et al., 2019] is doubly exponential in s.

Frank Ban, Xi Chen, Rocco A. Servedio, and Sandip Sinha. Efficient Average-Case Population Recovery in the Presence of Insertions and Deletions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 44:1-44:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ban_et_al:LIPIcs.APPROX-RANDOM.2019.44, author = {Ban, Frank and Chen, Xi and Servedio, Rocco A. and Sinha, Sandip}, title = {{Efficient Average-Case Population Recovery in the Presence of Insertions and Deletions}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)}, pages = {44:1--44:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-125-2}, ISSN = {1868-8969}, year = {2019}, volume = {145}, editor = {Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.44}, URN = {urn:nbn:de:0030-drops-112592}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2019.44}, annote = {Keywords: population recovery, deletion channel, trace reconstruction} }

Document

**Published in:** LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)

In this paper we present a generic reduction from the problem of finding an \epsilon-well-supported Nash equilibrium (WSNE) to that of finding an \Theta(\epsilon)-approximate Nash equilibrium (ANE), in large games with n players and a bounded number of strategies for each player.
Our reduction complements the existing literature on relations between WSNE and ANE, and can be applied to extend hardness results on WSNE to similar results on ANE.
This allows one to focus on WSNE first, which is in general easier to analyze and control in hardness constructions.
As an application we prove a 2^{\Omega(n/\log n)} lower bound on the randomized query complexity of finding an \epsilon-ANE in binary-action n-player games, for some constant \epsilon>0.
This answers an open problem posed by Hart and Nisan and Babichenko, and is very close to the trivial upper bound of 2^n.
Previously for WSNE, Babichenko showed a 2^{\Omega(n)} lower bound on the randomized query complexity of finding an \epsilon-WSNE for some constant epsilon>0.
Our result follows directly from combining Babichenko's result and our new reduction from WSNE to ANE.

Xi Chen, Yu Cheng, and Bo Tang. Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 57:1-57:9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.ITCS.2017.57, author = {Chen, Xi and Cheng, Yu and Tang, Bo}, title = {{Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games}}, booktitle = {8th Innovations in Theoretical Computer Science Conference (ITCS 2017)}, pages = {57:1--57:9}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-029-3}, ISSN = {1868-8969}, year = {2017}, volume = {67}, editor = {Papadimitriou, Christos H.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.57}, URN = {urn:nbn:de:0030-drops-81636}, doi = {10.4230/LIPIcs.ITCS.2017.57}, annote = {Keywords: Equilibrium Computation, Query Complexity, Large Games} }

Document

**Published in:** LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

In the problem of high-dimensional convexity testing, there is an unknown set S in the n-dimensional Euclidean space which is promised to be either convex or c-far from every convex body with respect to the standard multivariate normal distribution. The job of a testing algorithm is then to distinguish between these two cases while making as few inspections of the set S as possible.
In this work we consider sample-based testing algorithms, in which the testing algorithm only has access to labeled samples (x,S(x)) where each x is independently drawn from the normal distribution. We give nearly matching sample complexity upper and lower bounds for both one-sided and two-sided convexity testing algorithms in this framework. For constant c, our results show that the sample complexity of one-sided convexity testing is exponential in n, while for two-sided convexity testing it is exponential in the square root of n.

Xi Chen, Adam Freilich, Rocco A. Servedio, and Timothy Sun. Sample-Based High-Dimensional Convexity Testing. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 37:1-37:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.APPROX-RANDOM.2017.37, author = {Chen, Xi and Freilich, Adam and Servedio, Rocco A. and Sun, Timothy}, title = {{Sample-Based High-Dimensional Convexity Testing}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)}, pages = {37:1--37:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-044-6}, ISSN = {1868-8969}, year = {2017}, volume = {81}, editor = {Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.37}, URN = {urn:nbn:de:0030-drops-75867}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2017.37}, annote = {Keywords: Property testing, convexity, sample-based testing} }

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**Published in:** LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

We give a poly(log(n),1/epsilon)-query adaptive algorithm for testing whether an unknown Boolean function f:{-1, 1}^n -> {-1, 1}, which is promised to be a halfspace, is monotone versus epsilon-far from monotone. Since non-adaptive algorithms are known to require almost Omega(n^{1/2}) queries to test whether an unknown halfspace is monotone versus far from monotone, this shows that adaptivity enables an exponential improvement in the query complexity of monotonicity testing for halfspaces.

Xi Chen, Rocco A. Servedio, Li-Yang Tan, and Erik Waingarten. Adaptivity Is Exponentially Powerful for Testing Monotonicity of Halfspaces. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 38:1-38:21, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.APPROX-RANDOM.2017.38, author = {Chen, Xi and Servedio, Rocco A. and Tan, Li-Yang and Waingarten, Erik}, title = {{Adaptivity Is Exponentially Powerful for Testing Monotonicity of Halfspaces}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)}, pages = {38:1--38:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-044-6}, ISSN = {1868-8969}, year = {2017}, volume = {81}, editor = {Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.38}, URN = {urn:nbn:de:0030-drops-75877}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2017.38}, annote = {Keywords: property testing, linear threshold functions, monotonicity, adaptivity} }

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**Published in:** LIPIcs, Volume 79, 32nd Computational Complexity Conference (CCC 2017)

We prove that any non-adaptive algorithm that tests whether an unknown Boolean function f is a k-junta or epsilon-far from every k-junta must make ~Omega(k^{3/2}/ epsilon) many queries for a wide range of parameters k and epsilon. Our result dramatically improves previous lower bounds from [BGSMdW13,STW15], and is essentially optimal given Blais's non-adaptive junta tester from [Blais08], which makes ~O(k^{3/2})/epsilon queries. Combined with the adaptive tester of [Blais09] which makes O(k log k + k / epsilon) queries, our result shows that adaptivity enables polynomial savings in query complexity for junta testing.

Xi Chen, Rocco A. Servedio, Li-Yang Tan, Erik Waingarten, and Jinyu Xie. Settling the Query Complexity of Non-Adaptive Junta Testing. In 32nd Computational Complexity Conference (CCC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 79, pp. 26:1-26:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.CCC.2017.26, author = {Chen, Xi and Servedio, Rocco A. and Tan, Li-Yang and Waingarten, Erik and Xie, Jinyu}, title = {{Settling the Query Complexity of Non-Adaptive Junta Testing}}, booktitle = {32nd Computational Complexity Conference (CCC 2017)}, pages = {26:1--26:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-040-8}, ISSN = {1868-8969}, year = {2017}, volume = {79}, editor = {O'Donnell, Ryan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2017.26}, URN = {urn:nbn:de:0030-drops-75283}, doi = {10.4230/LIPIcs.CCC.2017.26}, annote = {Keywords: property testing, juntas, query complexity} }

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**Published in:** LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)

We study the complexity of approximation for a weighted counting constraint satisfaction problem #CSP(F). In the conservative case, where F contains all unary functions, a classification is known for the Boolean domain. We give a classification for problems with general finite domain. We define weak log-modularity and weak log-supermodularity, and show that #CSP(F) is in FP if F is weakly log-modular. Otherwise, it is at least as hard to approximate as #BIS, counting independent sets in bipartite graphs, which is believed to be intractable. We further sub-divide the #BIS-hard case. If F is weakly log-supermodular, we show that #CSP(F) is as easy as Boolean log-supermodular weighted #CSP. Otherwise, it is NP-hard to approximate. Finally, we give a trichotomy for the arity-2 case.
Then, #CSP(F) is in FP, is #BIS-equivalent, or is equivalent to #SAT, the problem of approximately counting satisfying assignments of a CNF Boolean formula.

Xi Chen, Martin Dyer, Leslie Ann Goldberg, Mark Jerrum, Pinyan Lu, Colin McQuillan, and David Richerby. The complexity of approximating conservative counting CSPs. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 148-159, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@InProceedings{chen_et_al:LIPIcs.STACS.2013.148, author = {Chen, Xi and Dyer, Martin and Goldberg, Leslie Ann and Jerrum, Mark and Lu, Pinyan and McQuillan, Colin and Richerby, David}, title = {{The complexity of approximating conservative counting CSPs}}, booktitle = {30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013)}, pages = {148--159}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-50-7}, ISSN = {1868-8969}, year = {2013}, volume = {20}, editor = {Portier, Natacha and Wilke, Thomas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.148}, URN = {urn:nbn:de:0030-drops-39303}, doi = {10.4230/LIPIcs.STACS.2013.148}, annote = {Keywords: counting constraint satisfaction problem, approximation, complexity} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 10281, Dynamically Reconfigurable Architectures (2010)

Scaling technology enables even higher degree of integration for FPGAs, but also brings new challenges that need to be addressed from both the architecture and the design tools side. Optimization of FPGA interconnection network is essential, given that interconnects dominate logic. Two approaches are presented, with one based on the time-multiplexing of wires and the other using hierarchical interconnects of high-speed serial links and switches. Design tools for both approaches are discussed. Preliminary experiments and prototypes are presented, and show positive results.

Xiaolei Chen and Yajun Ha. The Optimization of Interconnection Networks in FPGAs. In Dynamically Reconfigurable Architectures. Dagstuhl Seminar Proceedings, Volume 10281, pp. 1-9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2010)

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@InProceedings{chen_et_al:DagSemProc.10281.12, author = {Chen, Xiaolei and Ha, Yajun}, title = {{The Optimization of Interconnection Networks in FPGAs}}, booktitle = {Dynamically Reconfigurable Architectures}, pages = {1--9}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2010}, volume = {10281}, editor = {Peter M. Athanas and J\"{u}rgen Becker and J\"{u}rgen Teich and Ingrid Verbauwhede}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10281.12}, URN = {urn:nbn:de:0030-drops-28425}, doi = {10.4230/DagSemProc.10281.12}, annote = {Keywords: Field-programmable gate array, architecture, computer-aided design} }

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**Published in:** LIPIcs, Volume 17, Technical Communications of the 28th International Conference on Logic Programming (ICLP'12) (2012)

This paper extends action language C+ by introducing composite actions as sequential execution of other actions, leading to a more intuitive and flexible way to represent action domains, better exploit a general-purpose formalization, and improve the reasoning efficiency for large domains. Our experiments show that the composite actions can be seen as a method of knowledge acquisition for intelligent robots.

Xiaoping Chen, Guoqiang Jin, and Fangkai Yang. Extending C+ with Composite Actions for Robotic Task Planning. In Technical Communications of the 28th International Conference on Logic Programming (ICLP'12). Leibniz International Proceedings in Informatics (LIPIcs), Volume 17, pp. 404-414, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2012)

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@InProceedings{chen_et_al:LIPIcs.ICLP.2012.404, author = {Chen, Xiaoping and Jin, Guoqiang and Yang, Fangkai}, title = {{Extending C+ with Composite Actions for Robotic Task Planning}}, booktitle = {Technical Communications of the 28th International Conference on Logic Programming (ICLP'12)}, pages = {404--414}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-43-9}, ISSN = {1868-8969}, year = {2012}, volume = {17}, editor = {Dovier, Agostino and Santos Costa, V{\'\i}tor}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICLP.2012.404}, URN = {urn:nbn:de:0030-drops-36404}, doi = {10.4230/LIPIcs.ICLP.2012.404}, annote = {Keywords: Reasoning about Actions, Action Languages, Robotic Task Planning} }

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**Published in:** LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

A universal entangler (UE) is a unitary operation which maps all pure product states to entangled states. It is known that
for a bipartite system of particles 1,2 with a Hilbert space C^{d_1} otimes C^{d_2}, a UE exists when min(d_1,d_2) >= 3 and (d_1,d_2) != (3,3). It is also known that whenever a UE exists, almost all unitaries are UEs; however to verify whether a given unitary is a UE is very difficult since solving a quadratic system of equations is NP-hard in general. This work examines the existence and construction of UEs of bipartite bosonic/fermionic systems whose wave functions sit in the symmetric/antisymmetric subspace of C^d otimes C^d. The development of a theory of UEs for these types of systems needs considerably different approaches from that used for UEs of distinguishable systems. This is because the general entanglement of identical particle systems cannot be discussed in the usual way due to the effect of (anti)-symmetrization which introduces "pseudo entanglement" that is inaccessible in practice. We show that, unlike the distinguishable particle case, UEs exist for bosonic/fermionic systems with Hilbert spaces which are symmetric (resp. antisymmetric) subspaces of C^d otimes C^d if and only if d >= 3 (resp. d >= 8). To prove this we employ algebraic geometry to reason about the different algebraic structures of the bosonic/fermionic systems. Additionally, due to the relatively simple coherent state form of unentangled bosonic states, we are able to give the explicit constructions of two bosonic UEs. Our investigation provides insight into the entanglement properties of systems of indistinguishable particles, and in particular underscores the difference between the entanglement structures of bosonic, fermionic and distinguishable particle systems.

Joel Klassen, Jianxin Chen, and Bei Zeng. Universal Entanglers for Bosonic and Fermionic Systems. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 35-49, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@InProceedings{klassen_et_al:LIPIcs.TQC.2013.35, author = {Klassen, Joel and Chen, Jianxin and Zeng, Bei}, title = {{Universal Entanglers for Bosonic and Fermionic Systems}}, booktitle = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)}, pages = {35--49}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-55-2}, ISSN = {1868-8969}, year = {2013}, volume = {22}, editor = {Severini, Simone and Brandao, Fernando}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.35}, URN = {urn:nbn:de:0030-drops-43223}, doi = {10.4230/LIPIcs.TQC.2013.35}, annote = {Keywords: Universal Entangler, Bosonic States, Fermionic States} }

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**Published in:** LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

Symmetry is at the heart of coding theory. Codes with symmetry, especially cyclic codes, play an essential role in both theory and practical applications of classical error-correcting codes. Here we examine symmetry properties for codeword stabilized (CWS) quantum codes, which is the most general framework for constructing quantum error-correcting codes known to date. A CWS code Q can be represented by a self-dual additive code S and a classical code C, i.e., Q=(S,C), however this representation is in general not unique. We show that for any CWS code Q with certain permutation symmetry, one can always find a self-dual additive code S with the same permutation symmetry as Q such that Q=(S,C). As many good CWS codes have been found by starting from a chosen S, this ensures that when trying to find CWS codes with certain permutation symmetry, the choice of S with the same symmetry will suffice. A key step for this result is a new canonical representation for CWS codes, which is given in terms of a unique decomposition as union stabilizer codes. For CWS codes, so far mainly the standard form (G,C) has been considered, where G is a graph state. We analyze the symmetry of the corresponding graph of G, which in general cannot possess the same permutation symmetry as Q. We show that it is indeed the case for the toric code on a square lattice with translational symmetry, even if its encoding graph can be chosen to be translational invariant.

Salman Beigi, Jianxin Chen, Markus Grassl, Zhengfeng Ji, Qiang Wang, and Bei Zeng. Symmetries of Codeword Stabilized Quantum Codes. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 192-206, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

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@InProceedings{beigi_et_al:LIPIcs.TQC.2013.192, author = {Beigi, Salman and Chen, Jianxin and Grassl, Markus and Ji, Zhengfeng and Wang, Qiang and Zeng, Bei}, title = {{Symmetries of Codeword Stabilized Quantum Codes}}, booktitle = {8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)}, pages = {192--206}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-55-2}, ISSN = {1868-8969}, year = {2013}, volume = {22}, editor = {Severini, Simone and Brandao, Fernando}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.192}, URN = {urn:nbn:de:0030-drops-43129}, doi = {10.4230/LIPIcs.TQC.2013.192}, annote = {Keywords: CWS Codes, Union Stabilizer Codes, Permutation Symmetry, Toric Code} }

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Invited Paper

**Published in:** LIPIcs, Volume 139, 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)

K framework is an effort in realizing the ideal language framework where programming languages must have formal semantics and all languages tools are automatically generated from the formal semantics in a correct-by-construction manner at no additional costs. In this extended abstract, we present matching mu-logic as the foundation of K and discuss some of its applications in defining constructors, transition systems, modal mu-logic and temporal logic variants, and reachability logic.

Xiaohong Chen and Grigore Roşu. Matching mu-Logic: Foundation of K Framework (Invited Paper). In 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 139, pp. 1:1-1:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chen_et_al:LIPIcs.CALCO.2019.1, author = {Chen, Xiaohong and Ro\c{s}u, Grigore}, title = {{Matching mu-Logic: Foundation of K Framework}}, booktitle = {8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)}, pages = {1:1--1:4}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-120-7}, ISSN = {1868-8969}, year = {2019}, volume = {139}, editor = {Roggenbach, Markus and Sokolova, Ana}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2019.1}, URN = {urn:nbn:de:0030-drops-114296}, doi = {10.4230/LIPIcs.CALCO.2019.1}, annote = {Keywords: Matching mu-logic, Program verification, Reachability logic} }

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