Journal of the ACM最新文献

{"title":"The Price of Anarchy of Strategic Queuing Systems","authors":"Jason Gaitonde, Éva Tardos","doi":"https://dl.acm.org/doi/10.1145/3587250","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3587250","url":null,"abstract":"<p>Bounding the price of anarchy, which quantifies the damage to social welfare due to selfish behavior of the participants, has been an important area of research in algorithmic game theory. Classical work on such bounds in repeated games makes the strong assumption that the subsequent rounds of the repeated games are independent beyond any influence on play from past history. This work studies such bounds in environments that themselves change due to the actions of the agents. Concretely, we consider this problem in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet at each step to one of the servers, which will attempt to serve the oldest arriving packet, and unprocessed packets are returned to each queue. We model this as a repeated game where queues compete for the capacity of the servers, but where the state of the game evolves as the length of each queue varies.</p><p>We analyze this queuing system from multiple perspectives. As a baseline measure, we first establish precise conditions on the queuing arrival rates and service capacities that ensure all packets clear efficiently under centralized coordination. We then show that if queues strategically choose servers according to independent and stationary distributions, the system remains stable provided it would be stable under coordination with arrival rates scaled up by a factor of just (frac{e}{e-1}). Finally, we extend these results to no-regret learning dynamics: if queues use learning algorithms satisfying the no-regret property to choose servers, then the requisite factor increases to 2, and both of these bounds are tight. Both of these results require new probabilistic techniques compared to the classical price of anarchy literature and show that in such settings, no-regret learning can exhibit efficiency loss due to myopia.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"78 12","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525706","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Robustly Learning General Mixtures of Gaussians","authors":"Allen Liu, Ankur Moitra","doi":"https://dl.acm.org/doi/10.1145/3583680","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3583680","url":null,"abstract":"<p>This work represents a natural coalescence of two important lines of work — learning mixtures of Gaussians and algorithmic robust statistics. In particular, we give the first provably robust algorithm for learning mixtures of any constant number of Gaussians. We require only mild assumptions on the mixing weights and that the total variation distance between components is bounded away from zero. At the heart of our algorithm is a new method for proving a type of dimension-independent polynomial identifiability — which we call robust identifiability — through applying a carefully chosen sequence of differential operations to certain generating functions that not only encode the parameters we would like to learn but also the system of polynomial equations we would like to solve. We show how the symbolic identities we derive can be directly used to analyze a natural sum-of-squares relaxation.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"54 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525678","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Stochastic Games with Synchronization Objectives","authors":"Laurent Doyen","doi":"https://dl.acm.org/doi/10.1145/3588866","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3588866","url":null,"abstract":"<p>We consider two-player stochastic games played on a finite graph for infinitely many rounds. Stochastic games generalize both Markov decision processes (MDP) by adding an adversary player, and two-player deterministic games by adding stochasticity. The outcome of the game is a sequence of distributions over the graph states, representing the evolution of a population consisting of a continuum number of identical copies of a process modeled by the game graph. We consider synchronization objectives, which require the probability mass to accumulate in a set of target states, either always, once, infinitely often, or always after some point in the outcome sequence; and the winning modes of sure winning (if the accumulated probability is equal to 1) and almost-sure winning (if the accumulated probability is arbitrarily close to 1).</p><p>We present algorithms to compute the set of winning distributions for each of these synchronization modes, showing that the corresponding decision problem is PSPACE-complete for synchronizing once and infinitely often and PTIME-complete for synchronizing always and always after some point. These bounds are remarkably in line with the special case of MDPs, while the algorithmic solution and proof technique are considerably more involved, even for deterministic games. This is because those games have a flavor of imperfect information, in particular they are not determined and randomized strategies need to be considered, even if there is no stochastic choice in the game graph. Moreover, in combination with stochasticity in the game graph, finite-memory strategies are not sufficient in general.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"45 6","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"The One-Way Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness","authors":"Moran Feldman, Ashkan Norouzi-Fard, Ola Svensson, Rico Zenklusen","doi":"https://dl.acm.org/doi/10.1145/3588564","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3588564","url":null,"abstract":"<p>We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multi-player model that lies between the offline and streaming model, and study it under the aspect of one-way communication complexity. Our model captures the streaming setting (by considering a large number of players), and, in addition, two player approximation results for it translate into the robust setting. We present tight one-way communication complexity results for our model, which, due to the above-mentioned connections, have multiple implications in the data stream and robust setting. </p><p>Even for just two players, a prior information-theoretic hardness result implies that no approximation factor above 1/2 can be achieved in our model, if only queries to feasible sets, i.e., sets respecting the cardinality constraint, are allowed. We show that the possibility of querying infeasible sets can actually be exploited to beat this bound, by presenting a tight 2/3-approximation taking exponential time, and an efficient 0.514-approximation. To the best of our knowledge, this is the first example where querying a submodular function on infeasible sets leads to provably better results. Through the above-mentioned link to the (non-streaming) robust setting, both of these algorithms improve on the current state-of-the-art for robust submodular maximization, showing that approximation factors beyond 1/2 are possible. Moreover, exploiting the link of our model to streaming, we settle the approximability for streaming algorithms by presenting a tight 1/2 + ε hardness result, based on the construction of a new family of coverage functions. This improves on a prior 0.586 hardness and matches, up to an arbitrarily small margin, the best known approximation algorithm.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"30 9-10","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"The One-Way Communication Complexity of Submodular Maximization with Applications to Streaming and Robustness","authors":"Moran Feldman, A. Norouzi-Fard, O. Svensson, R. Zenklusen","doi":"10.1145/3588564","DOIUrl":"https://doi.org/10.1145/3588564","url":null,"abstract":"We consider the classical problem of maximizing a monotone submodular function subject to a cardinality constraint, which, due to its numerous applications, has recently been studied in various computational models. We consider a clean multiplayer model that lies between the offline and streaming model, and study it under the aspect of one-way communication complexity. Our model captures the streaming setting (by considering a large number of players), and, in addition, two-player approximation results for it translate into the robust setting. We present tight one-way communication complexity results for our model, which, due to the connections mentioned previously, have multiple implications in the data stream and robust setting. Even for just two players, a prior information-theoretic hardness result implies that no approximation factor above 1/2 can be achieved in our model, if only queries to feasible sets (i.e., sets respecting the cardinality constraint) are allowed. We show that the possibility of querying infeasible sets can actually be exploited to beat this bound, by presenting a tight 2/3-approximation taking exponential time, and an efficient 0.514-approximation. To the best of our knowledge, this is the first example where querying a submodular function on infeasible sets leads to provably better results. Through the link to the (non-streaming) robust setting mentioned previously, both of these algorithms improve on the current state of the art for robust submodular maximization, showing that approximation factors beyond 1/2 are possible. Moreover, exploiting the link of our model to streaming, we settle the approximability for streaming algorithms by presenting a tight 1/2+ɛ hardness result, based on the construction of a new family of coverage functions. This improves on a prior 0.586 hardness and matches, up to an arbitrarily small margin, the best-known approximation algorithm.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"115 1","pages":"1 - 52"},"PeriodicalIF":2.5,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80286072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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 Exponential-time Hypotheses, Derandomization, and Circuit Lower Bounds","authors":"Lijie Chen, Ron Rothblum, Roei Tell, Eylon Yogev","doi":"10.1145/3593581","DOIUrl":"https://doi.org/10.1145/3593581","url":null,"abstract":"The Exponential-Time Hypothesis (ETH) is a strengthening of the 𝒫 ≠ 𝒩𝒫 conjecture, stating that 3- SAT on n variables cannot be solved in (uniform) time 2 εċ n , for some ε &gt; 0. In recent years, analogous hypotheses that are “exponentially strong” forms of other classical complexity conjectures (such as 𝒩𝒫⊈ ℬ𝒫𝒫 or co 𝒩𝒫⊈𝒩𝒫) have also been introduced and have become widely influential. In this work, we focus on the interaction of exponential-time hypotheses with the fundamental and closely related questions of derandomization and circuit lower bounds . We show that even relatively mild variants of exponential-time hypotheses have far-reaching implications to derandomization, circuit lower bounds, and the connections between the two. Specifically, we prove that: (1) The Randomized Exponential-Time Hypothesis (rETH) implies that ℬ𝒫𝒫 can be simulated on “average-case” in deterministic (nearly-)polynomial-time (i.e., in time 2 Õ(log( n )) = n loglog( n ) O(1) ). The derandomization relies on a conditional construction of a pseudorandom generator with near-exponential stretch (i.e., with seed length Õ(log ( n ))); this significantly improves the state-of-the-art in uniform “hardness-to-randomness” results, which previously only yielded pseudorandom generators with sub-exponential stretch from such hypotheses. (2) The Non-Deterministic Exponential-Time Hypothesis (NETH) implies that derandomization of ℬ𝒫𝒫 is completely equivalent to circuit lower bounds against ℰ, and in particular that pseudorandom generators are necessary for derandomization. In fact, we show that the foregoing equivalence follows from a very weak version of NETH, and we also show that this very weak version is necessary to prove a slightly stronger conclusion that we deduce from it. Last, we show that disproving certain exponential-time hypotheses requires proving breakthrough circuit lower bounds. In particular, if CircuitSAT for circuits over n bits of size poly(n) can be solved by probabilistic algorithms in time 2 n /polylog(n) , then ℬ𝒫ℰ does not have circuits of quasilinear size.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135568383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Intermediate Value Linearizability: A Quantitative Correctness Criterion","authors":"Arik Rinberg, Idit Keidar","doi":"https://dl.acm.org/doi/10.1145/3584699","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3584699","url":null,"abstract":"&lt;p&gt;Big data processing systems often employ batched updates and data sketches to estimate certain properties of large data. For example, a &lt;i&gt;CountMin sketch&lt;/i&gt; approximates the frequencies at which elements occur in a data stream, and a &lt;i&gt;batched counter&lt;/i&gt; counts events in batches. This article focuses on correctness criteria for concurrent implementations of such objects. Specifically, we consider &lt;i&gt;quantitative&lt;/i&gt; objects, whose return values are from an ordered domain, with a particular emphasis on &lt;i&gt;(ε,δ)-bounded&lt;/i&gt; objects that estimate a numerical quantity with an error of at most ε with probability at least 1 - δ.&lt;/p&gt;&lt;p&gt;The de facto correctness criterion for concurrent objects is linearizability. Intuitively, under linearizability, when a read overlaps an update, it must return the object’s value either before the update or after it. Consider, for example, a single batched increment operation that counts three new events, bumping a batched counter’s value from 7 to 10. In a linearizable implementation of the counter, a read overlapping this update must return either 7 or 10. We observe, however, that in typical use cases, any &lt;i&gt;intermediate&lt;/i&gt; value between 7 and 10 would also be acceptable. To capture this additional degree of freedom, we propose &lt;i&gt;Intermediate Value Linearizability (IVL)&lt;/i&gt;, a new correctness criterion that relaxes linearizability to allow returning intermediate values, for instance, 8 in the example above. Roughly speaking, IVL allows reads to return any value that is bounded between two return values that are legal under linearizability.&lt;/p&gt;&lt;p&gt;A key feature of IVL is that we can prove that concurrent IVL implementations of (ε,δ)-bounded objects are themselves (ε,δ)-bounded. To illustrate the power of this result, we give a straightforward and efficient concurrent implementation of an (ε,δ)-bounded CountMin sketch, which is IVL (albeit not linearizable).&lt;/p&gt;&lt;p&gt;We present four examples for IVL objects, each showcasing a different way of using IVL. The first is a simple wait-free IVL batched counter, with &lt;i&gt;O&lt;/i&gt;(1) step complexity for update. The next considers an (ε,δ)-bounded CountMin sketch and further shows how to relax IVL using the notion of &lt;i&gt;r&lt;/i&gt;-relaxation. Our third example is a non-atomic iterator over a data structure. In this example, we augment the data structure with an &lt;i&gt;auxiliary history variable&lt;/i&gt; state that includes “tombstones” for items deleted from the data structure. Here, IVL semantics are required at the augmented level. Finally, using a &lt;i&gt;priority queue&lt;/i&gt;, we show that some objects require IVL to be paired with other correctness criteria; indeed, a natural correctness notion for a concurrent priority queue is IVL coupled with sequential consistency.&lt;/p&gt;&lt;p&gt;Last, we show that IVL allows for inherently cheaper implementations than linearizable ones. In particular, we show a lower bound of Ω (&lt;i&gt;n&lt;/i&gt;) on the step complexity of the update operation of any wait-free linearizable","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"43 11-12","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Lower Bounds for Semialgebraic Range Searching and Stabbing Problems","authors":"Peyman Afshani, Pingan Cheng","doi":"https://dl.acm.org/doi/10.1145/3578574","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3578574","url":null,"abstract":"&lt;p&gt;In the semialgebraic range searching problem, we are given a set of &lt;i&gt;n&lt;/i&gt; points in ℝ&lt;sup&gt;&lt;i&gt;d&lt;/i&gt;&lt;/sup&gt;, and we want to preprocess the points such that for any query range belonging to a family of constant complexity semialgebraic sets (Tarski cells), all the points intersecting the range can be reported or counted efficiently. When the ranges are composed of simplices, the problem is well-understood: It can be solved using &lt;i&gt;S(n)&lt;/i&gt; space and with &lt;i&gt;Q(n)&lt;/i&gt; query time with (S(n)Q(n)^d = tilde{O}(n^d),) where the (tilde{O}(cdot)) notation hides polylogarithmic factors and this trade-off is tight (up to &lt;i&gt;n&lt;/i&gt;&lt;sup&gt;&lt;i&gt;o&lt;/i&gt;(1)&lt;/sup&gt; factors). In particular, there exist “low space” structures that use &lt;i&gt;O(n)&lt;/i&gt; space with &lt;i&gt;O&lt;/i&gt;(&lt;i&gt;n&lt;/i&gt;&lt;sup&gt;1-1/&lt;i&gt;d&lt;/i&gt;}&lt;/sup&gt;) query time [8, 25] and “fast query” structures that use &lt;i&gt;O&lt;/i&gt;(&lt;i&gt;n&lt;/i&gt;&lt;sup&gt;&lt;i&gt;d&lt;/i&gt;&lt;/sup&gt;) space with &lt;i&gt;O&lt;/i&gt;(log &lt;i&gt;n&lt;/i&gt;) query time [9]. However, for general semialgebraic ranges, only “low space” solutions are known, but the best solutions [7] match the same trade-off curve as simplex queries, with &lt;i&gt;O&lt;/i&gt;(&lt;i&gt;n&lt;/i&gt;) space and (tilde{O}(n^{1-1/d})) query time. It has been conjectured that the same could be done for the “fast query” case, but this open problem has stayed unresolved.&lt;/p&gt;&lt;p&gt;Here, we disprove this conjecture. We give the first nontrivial lower bounds for semialgebraic range searching and other related problems. More precisely, we show that any data structure for reporting the points between two concentric circles, a problem that we call 2D annulus reporting, with &lt;i&gt;Q&lt;/i&gt;(&lt;i&gt;n&lt;/i&gt;) query time must use (S(n)=overset{scriptscriptstyle o}{Omega }(n^3/Q(n)^5)) space, where the (overset{scriptscriptstyle o}{Omega }(cdot)) notation hides (n^{o(1)}) factors, meaning, for (Q(n)=log ^{O(1)}n), (overset{scriptscriptstyle o}{Omega }(n^3)) space must be used. In addition, we study the problem of reporting the subset of input points in a polynomial slab defined by (lbrace (x,y)in mathbb {R}^2:P(x)le yle P(x)+wrbrace), where (P(x)=sum _{i=0}^Delta a_i x^i) is a univariate polynomial of degree Δ and (a_0, ldots , a_Delta , w) are given at the query time, a problem that we call polynomial slab reporting. For this, we show a space lower bound of (overset{scriptscriptstyle o}{Omega }(n^{Delta +1}/Q(n)^{(Delta +3)Delta /2})), which implies that for (Q(n)=log ^{O(1)}n), we must use (overset{scriptscriptstyle o}{Omega }(n^{Delta +1})) space. We also consider the dual semialgebraic stabbing problems of semialgebraic range searching and present lower bounds for them. In particular, we show that in linear space, any data structure that solves 2D annulus stabbing problems must use (Omega (n^{2/3})) query time. Note that this almost matches the upper bound obtained by lifting 2D annuli to 3D. Like semialgebraic range searching, we also present lower bounds for general polynomial slab stabbing problems. Again, our lower bounds are almost tight for linear size data structures in th","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"45 9","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Lower Bounds on Implementing Mediators in Asynchronous Systems with Rational and Malicious Agents","authors":"Ivan Geffner, Joseph Y. Halpern","doi":"https://dl.acm.org/doi/10.1145/3578579","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3578579","url":null,"abstract":"<p>Abraham, Dolev, Geffner, and Halpern [1] proved that, in asynchronous systems, a <i>(k, t)-robust equilibrium</i> for <i>n</i> players and a trusted mediator can be implemented without the mediator as long as <i>n</i> &gt; 4(<i>k+t</i>), where an equilibrium is (<i>k, t</i>)-robust if, roughly speaking, no coalition of <i>t</i> players can decrease the payoff of any of the other players, and no coalition of <i>k</i> players can increase their payoff by deviating. We prove that this bound is tight, in the sense that if <i>n</i> ≤ 4(<i>k+t</i>) there exist (<i>k, t</i>)-robust equilibria with a mediator that cannot be implemented by the players alone. Even though implementing (<i>k, t</i>)-robust mediators seems closely related to implementing asynchronous multiparty (<i>k+t</i>)-secure computation [6], to the best of our knowledge there is no known straightforward reduction from one problem to another. Nevertheless, we show that there is a non-trivial reduction from a slightly weaker notion of (<i>k+t</i>)-secure computation, which we call <i>(<i>k+t</i>)-strict secure computation</i>, to implementing (<i>k, t</i>)-robust mediators. We prove the desired lower bound by showing that there are functions on <i>n</i> variables that cannot be (<i>k+t</i>)-strictly securely computed if <i>n</i> ≤ 4(<i>k+t</i>). This also provides a simple alternative proof for the well-known lower bound of 4<i>t</i>+1 on asynchronous secure computation in the presence of up to <i>t</i> malicious agents [4, 8, 10].</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"19 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"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":"Separating Rank Logic from Polynomial Time","authors":"Moritz Lichter","doi":"https://dl.acm.org/doi/10.1145/3572918","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3572918","url":null,"abstract":"<p>In the search for a logic capturing polynomial time the most promising candidates are Choiceless Polynomial Time (CPT) and rank logic. Rank logic extends fixed-point logic with counting by a rank operator over prime fields. We show that the isomorphism problem for CFI graphs over ℤ_2^<i>i</i> cannot be defined in rank logic, even if the base graph is totally ordered. However, CPT can define this isomorphism problem. We thereby separate rank logic from CPT and in particular from polynomial time.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"32 7-8","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}