Information and Computation最新文献

{"title":"Automating approximation analysis for Nash equilibria algorithms in two-player games","authors":"Xiaotie Deng ,&nbsp;Dongchen Li ,&nbsp;Hanyu Li","doi":"10.1016/j.ic.2025.105362","DOIUrl":"10.1016/j.ic.2025.105362","url":null,"abstract":"<div><div>Computing polynomial-time approximate Nash equilibria (NE) is a fundamental problem in algorithmic game theory, with deep connections to the complexity class TFNP. Recent advances in approximate NE algorithms have become increasingly sophisticated, making the verification of their approximation guarantees both complex and error-prone. We present the first automated method for analyzing approximation bounds of algorithms for two-player normal-form games. Given any algorithm that computes approximate NE, our approach automatically derives tight approximation bounds using constraint programming techniques. We demonstrate the effectiveness of our method by applying it to all known algorithms in the literature, reproducing their manually-proven approximation bounds within seconds and without human intervention. Our results provide both a powerful verification tool and new insights into the structure of approximate equilibrium computation.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105362"},"PeriodicalIF":1.0,"publicationDate":"2025-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266908","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Monotonicity characterizations of regular languages","authors":"Yoav Feinstein,&nbsp;Orna Kupferman","doi":"10.1016/j.ic.2025.105360","DOIUrl":"10.1016/j.ic.2025.105360","url":null,"abstract":"<div><div>Each language <span><math><mi>L</mi><mo>⊆</mo><msup><mrow><mi>Σ</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span> induces an infinite sequence <span><math><msubsup><mrow><mo>{</mo><mi>P</mi><mi>r</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span>, where for all <span><math><mi>n</mi><mo>≥</mo><mn>1</mn></math></span>, the value <span><math><mi>P</mi><mi>r</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>]</mo></math></span> is the probability of a word of length <em>n</em> to be in <em>L</em>, assuming a uniform distribution on the letters in Σ. Previous studies of <span><math><msubsup><mrow><mo>{</mo><mi>P</mi><mi>r</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span> for a regular language <em>L</em>, concerned zero-one laws, density, and accumulation points. We study monotonicity of <span><math><msubsup><mrow><mo>{</mo><mi>P</mi><mi>r</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>n</mi><mo>)</mo><mo>}</mo></mrow><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mrow><mo>∞</mo></mrow></msubsup></math></span>, possibly in the limit. We show that monotonicity may depend on the distribution of letters, study how operations on languages affect monotonicity, and characterize classes of languages for which the sequence is monotonic. We extend the study to languages <em>L</em> of infinite words, where we study the probability of lasso-shaped words to be in <em>L</em> and consider two definitions for <span><math><mi>P</mi><mi>r</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></span>. The first refers to the probability of prefixes of length <em>n</em> to be extended to words in <em>L</em>, and the second to the probability of word <em>w</em> of length <em>n</em> to be such that <span><math><msup><mrow><mi>w</mi></mrow><mrow><mi>ω</mi></mrow></msup></math></span> is in <em>L</em>. Thus, in the second definition, monotonicity depends not only on the length of <em>w</em>, but also on the words being periodic. We also study the complexity of calculating <span><math><mi>P</mi><mi>r</mi><mo>(</mo><mi>L</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></span> for the various definitions.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105360"},"PeriodicalIF":1.0,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266164","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Unbounded quantum-classical separation in sample complexity for sphere center finding","authors":"Guanzhong Li ,&nbsp;Lvzhou Li","doi":"10.1016/j.ic.2025.105361","DOIUrl":"10.1016/j.ic.2025.105361","url":null,"abstract":"<div><div>Fast quantum algorithms can solve important computational problems more efficiently than classical algorithms. However, little is known about whether quantum computing can speed up solving geometric problems. This article explores quantum advantages for the problem of finding the center of a sphere in vector spaces over finite fields, given samples of random points on the sphere. We prove that any classical algorithm for this task requires approximately as many samples as the dimension of the vector space, by a reduction to an old and basic algebraic result—Warning's second theorem. On the other hand, we propose a quantum algorithm based on quantum walks that needs only a constant number of samples to find the center. Thus, an unbounded quantum advantage is revealed for a natural and intuitive geometric problem, which highlights the power of quantum computing in solving geometric problems.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105361"},"PeriodicalIF":1.0,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266909","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Intersection and union hierarchies of deterministic context-free languages and pumping lemmas","authors":"Tomoyuki Yamakami","doi":"10.1016/j.ic.2025.105358","DOIUrl":"10.1016/j.ic.2025.105358","url":null,"abstract":"<div><div>We study the computational complexity of finite intersections and finite unions of deterministic context-free (dcf) languages. Earlier, Wotschke [J. Comput. System Sci. 16 (1978) 456–461] demonstrated that intersections of <span><math><mo>(</mo><mi>d</mi><mo>+</mo><mn>1</mn><mo>)</mo></math></span> dcf languages are in general more powerful than intersections of <em>d</em> dcf languages for any positive integer <em>d</em> based on the separation result of the intersection hierarchy of Liu and Weiner [Math. Systems Theory 7 (1973) 185–192]. The argument of Liu and Weiner, however, works only on bounded languages of particular forms, and therefore Wotschke's result is not directly extendable to other non-bounded languages. To deal with a wide range of languages for the non-membership to the intersection hierarchy, we circumvent the specialization of their proof technics and devise a new and practical technical tool: two pumping lemmas for finite unions of dcf languages. Since the family of dcf languages is closed under complementation and also under intersection with regular languages, these pumping lemmas help us establish the non-membership relation of languages formed by finite intersections of target languages. We also concern ourselves with a relationship to deterministic limited automata of Hibbard [Inf. Control 11 (1967) 196–238] in this regard.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105358"},"PeriodicalIF":1.0,"publicationDate":"2025-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145266910","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Assumptions of randomness in cosmology models","authors":"Leonid A. Levin","doi":"10.1016/j.ic.2025.105359","DOIUrl":"10.1016/j.ic.2025.105359","url":null,"abstract":"<div><div>Non-compact symmetries cannot be fully broken by randomness since non-compact groups have no invariant probability distributions. In particular, this makes trickier the “Copernican” random choice of the place of the observer in infinite cosmology models.</div><div>This problem may be circumvented with what topologists call <em>pointed spaces</em>. Then randomness will be used only in building (infinite) models around the pre-designated “observance point”, that thus would not need to be randomly chosen.</div><div>Additional complications come from the original randomness possibly being hidden. P. Gacs and A. Kucera proved that every sequence can be algorithmically generated from a random one. But Vladimir V'yugin discovered that randomized algorithms can with positive probability generate uncomputable sequences not algorithmically equivalent to any random ones.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105359"},"PeriodicalIF":1.0,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145220325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Recent algorithmic advances in simple temporal networks with uncertainty: From faster controllability checking to faster execution","authors":"Luke Hunsberger ,&nbsp;Roberto Posenato","doi":"10.1016/j.ic.2025.105356","DOIUrl":"10.1016/j.ic.2025.105356","url":null,"abstract":"<div><div>This paper advances the state of the art in the dynamic controllability (DC) and dispatchability of Simple Temporal Networks with Uncertainty (STNUs) through four key contributions.</div><div>First, <span>findSRNC</span> is an algorithm that identifies semi-reducible negative cycles in non-dynamically controllable STNUs. Running in <span><math><mi>O</mi><mo>(</mo><mi>m</mi><mi>n</mi><mo>+</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>n</mi><mo>+</mo><mi>k</mi><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time (matching the fastest DC-checking algorithms), it handles repeated edges and uses polynomial space, even when cycles might contain exponentially many edges.</div><div>Second, <span>minDisp</span><span><math><msubsup><mrow></mrow><mrow><mi>ESTNU</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span> is an algorithm that improves dispatchability computation for STNUs from <span><math><mi>O</mi><mo>(</mo><mi>k</mi><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>)</mo></math></span> to <span><math><mi>O</mi><mo>(</mo><msup><mrow><mi>n</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>+</mo><msup><mrow><mi>k</mi></mrow><mrow><mn>2</mn></mrow></msup><mi>n</mi><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span> time. It outputs dispatchable Extended STNUs (ESTNUs) having minimal numbers of edges, which is crucial for subsequent real-time execution.</div><div>Third, the Canonical Form of Nested Diamond Structures in Dispatchable ESTNUs is a rigorous theory that facilitates correctness proofs for dispatchability algorithms. It also helped reveal and correct a flaw in a previously published algorithm.</div><div>Fourth, our empirical evaluation using improved open-source implementations demonstrates the practical effectiveness of our algorithms.</div><div>These contributions address fundamental computational bottlenecks in temporal planning systems, enabling more efficient reasoning about uncertain timing constraints while providing real-time guarantees required for robotics, scheduling, and automated planning applications.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105356"},"PeriodicalIF":1.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145158783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"k-Universality of Regular Languages","authors":"Duncan Adamson ,&nbsp;Pamela Fleischmann ,&nbsp;Annika Huch ,&nbsp;Tore Koß ,&nbsp;Florin Manea ,&nbsp;Dirk Nowotka","doi":"10.1016/j.ic.2025.105357","DOIUrl":"10.1016/j.ic.2025.105357","url":null,"abstract":"<div><div>A subsequence of a word <em>w</em> is a word <em>u</em> such that <span><math><mi>u</mi><mo>=</mo><mi>w</mi><mo>[</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>]</mo><mi>w</mi><mo>[</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>]</mo><mo>…</mo><mi>w</mi><mo>[</mo><msub><mrow><mi>i</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>]</mo></math></span>, for some set of indices <span><math><mn>1</mn><mo>≤</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>&lt;</mo><msub><mrow><mi>i</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>&lt;</mo><mo>…</mo><mo>&lt;</mo><msub><mrow><mi>i</mi></mrow><mrow><mi>k</mi></mrow></msub><mo>≤</mo><mo>|</mo><mi>w</mi><mo>|</mo></math></span>. A word <em>w</em> is <em>k</em>-subsequence universal over an alphabet Σ if every word in <span><math><msup><mrow><mi>Σ</mi></mrow><mrow><mi>k</mi></mrow></msup></math></span> appears in <em>w</em> as a subsequence. In this paper, we study the intersection between the set of <em>k</em>-subsequence universal words over some alphabet Σ and regular languages over Σ. We call a regular language <em>L k-</em>∃<em>-subsequence universal</em> if there exists a <em>k</em>-subsequence universal word in <em>L</em>, and <em>k-</em>∀<em>-subsequence universal</em> if every word of <em>L</em> is <em>k</em>-subsequence universal. We give algorithms solving the problems of deciding if a given regular language, represented by a finite automaton recognising it, is <em>k-</em>∃<em>-subsequence universal</em> and, respectively, if it is <em>k-</em>∀<em>-subsequence universal</em>, for a given <em>k</em>. The algorithms are FPT w.r.t. the size of the input alphabet, and their run-time does not depend on <em>k</em>; they run in polynomial time in the number <em>n</em> of states of the input automaton when the size of the input alphabet is <span><math><mi>O</mi><mo>(</mo><mi>log</mi><mo>⁡</mo><mi>n</mi><mo>)</mo></math></span>. Moreover, we show that the problem of deciding if a given regular language is <em>k-</em>∃<em>-subsequence universal</em> is NP-complete, when the language is over a large alphabet. Further, we provide algorithms for counting the number of <em>k</em>-subsequence universal words (paths) accepted by a given deterministic (respectively, non-deterministic) finite automaton, and ranking an input word (path) within the set of <em>k</em>-subsequence universal words accepted by a given finite automaton.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105357"},"PeriodicalIF":1.0,"publicationDate":"2025-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145120853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Polynomial Turing compressions for some graph problems parameterized by modular-width","authors":"Weidong Luo","doi":"10.1016/j.ic.2025.105355","DOIUrl":"10.1016/j.ic.2025.105355","url":null,"abstract":"<div><div>A polynomial Turing compression (PTC) for a parameterized problem <em>L</em> is a polynomial time Turing machine that has access to an oracle for a problem <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>′</mo></mrow></msup></math></span> such that a polynomial in the input parameter bounds each query. Meanwhile, a polynomial compression (PC) can be regarded as a restricted variant of PTC where the machine can query the oracle exactly once and must output the same answer as the oracle. Bodlaender et al. (ICALP 2008) and Fortnow and Santhanam (STOC 2008) initiated an impressive hardness theory for PC under the assumption coNP ⊈ NP/poly. Let <span><math><mi>C</mi></math></span> be the set of all problems with PTCs but without PCs assuming coNP ⊈ NP/poly. Fernau et al. (STACS 2009) identified <span>Leaf Out-tree(</span><em>k</em><span>)</span> as the first problem in <span><math><mi>C</mi></math></span>. However, little is known about <span><math><mi>C</mi></math></span>, with only a dozen problems confirmed in it over the last fifteen years. Open questions remain, such as whether CNF-SAT(<em>n</em>) and <em>k</em>-path are in <span><math><mi>C</mi></math></span>, requiring novel ideas to clarify the differences between PTCs and PCs.</div><div>In this paper, we enrich our knowledge about <span><math><mi>C</mi></math></span> by demonstrating that 17 problems parameterized by modular-width (<em>mw</em>), such as <span>Chromatic Number(</span><em>mw</em><span>)</span> and <span>Hamiltonian Cycle(</span><em>mw</em><span>)</span>, belong to <span><math><mi>C</mi></math></span>. Additionally, we develop a general recipe to prove the existence of PTCs for a class of problems, including these 17.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105355"},"PeriodicalIF":1.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145105713","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On cardinalities of Rogers semilattices for families in the Ershov hierarchy","authors":"Keng Meng Ng ,&nbsp;Nikolay Bazhenov ,&nbsp;Birzhan Kalmurzayev ,&nbsp;Dias Nurlanbek","doi":"10.1016/j.ic.2025.105354","DOIUrl":"10.1016/j.ic.2025.105354","url":null,"abstract":"<div><div>The theory of numberings provides classification results for families of sets in various computability-theoretic hierarchies. The algorithmic content of numberings is typically calibrated via the reducibility between numberings. For a given family of sets <em>S</em>, this reducibility gives rise to an upper semilattice of degrees that is often called the Rogers semilattice of <em>S</em>.</div><div>This paper studies the cardinalities of Rogers semilattices for families of sets at finite levels of the Ershov hierarchy. The classical result of Khutoretskii (1971) shows that the Rogers semilattice of a family of c.e. sets is either one-element or countably infinite. Badaev and Lempp (2009) constructed a family of d.c.e. sets that demonstrates that the methods of Khutoretskii cannot be applied to obtain a similar result for Rogers semilattices already at the second level of the Ershov hierarchy.</div><div>We prove that for any finite family of sets <em>S</em> at any finite level of the Ershov hierarchy, the corresponding Rogers semilattice is either one-element or countably infinite. We also obtain another sufficient condition for a Rogers semilattice to be infinite. This condition implies that the Rogers semilattice of Badaev and Lempp is also infinite.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105354"},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048896","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Competition among parallel contests","authors":"Xiaotie Deng ,&nbsp;Ningyuan Li ,&nbsp;Weian Li ,&nbsp;Qi Qi","doi":"10.1016/j.ic.2025.105339","DOIUrl":"10.1016/j.ic.2025.105339","url":null,"abstract":"<div><div>We investigate the model of multiple rank-order contests held in parallel, where each contestant only selects one contest to join and each contest designer decides the prize structure to compete for the participation of contestants. We first analyze the strategic behaviors of contestants and completely characterize the symmetric Bayesian Nash equilibrium. As for the strategies of contest designers, when other designers' strategies are known, we show that computing the best response is NP-hard and propose a fully polynomial time approximation scheme to output the <em>ϵ</em>-approximate best response. When other designers' strategies are unknown, we provide a worst-case analysis on one designer's strategy. We give an upper bound on the worst-case utility of any strategy and propose a method to construct a strategy whose utility can guarantee a constant ratio of this upper bound in the worst case.</div></div>","PeriodicalId":54985,"journal":{"name":"Information and Computation","volume":"307 ","pages":"Article 105339"},"PeriodicalIF":1.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145048822","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}