@inproceedings{141, abstract = {Given a model and a specification, the fundamental model-checking problem asks for algorithmic verification of whether the model satisfies the specification. We consider graphs and Markov decision processes (MDPs), which are fundamental models for reactive systems. One of the very basic specifications that arise in verification of reactive systems is the strong fairness (aka Streett) objective. Given different types of requests and corresponding grants, the objective requires that for each type, if the request event happens infinitely often, then the corresponding grant event must also happen infinitely often. All ω -regular objectives can be expressed as Streett objectives and hence they are canonical in verification. To handle the state-space explosion, symbolic algorithms are required that operate on a succinct implicit representation of the system rather than explicitly accessing the system. While explicit algorithms for graphs and MDPs with Streett objectives have been widely studied, there has been no improvement of the basic symbolic algorithms. The worst-case numbers of symbolic steps required for the basic symbolic algorithms are as follows: quadratic for graphs and cubic for MDPs. In this work we present the first sub-quadratic symbolic algorithm for graphs with Streett objectives, and our algorithm is sub-quadratic even for MDPs. Based on our algorithmic insights we present an implementation of the new symbolic approach and show that it improves the existing approach on several academic benchmark examples.}, author = {Chatterjee, Krishnendu and Henzinger, Monika H and Loitzenbauer, Veronika and Oraee, Simin and Toman, Viktor}, location = {Oxford, United Kingdom}, pages = {178--197}, publisher = {Springer}, title = {{Symbolic algorithms for graphs and Markov decision processes with fairness objectives}}, doi = {10.1007/978-3-319-96142-2_13}, volume = {10982}, year = {2018}, } @inproceedings{143, abstract = {Vector Addition Systems with States (VASS) provide a well-known and fundamental model for the analysis of concurrent processes, parameterized systems, and are also used as abstract models of programs in resource bound analysis. In this paper we study the problem of obtaining asymptotic bounds on the termination time of a given VASS. In particular, we focus on the practically important case of obtaining polynomial bounds on termination time. Our main contributions are as follows: First, we present a polynomial-time algorithm for deciding whether a given VASS has a linear asymptotic complexity. We also show that if the complexity of a VASS is not linear, it is at least quadratic. Second, we classify VASS according to quantitative properties of their cycles. We show that certain singularities in these properties are the key reason for non-polynomial asymptotic complexity of VASS. In absence of singularities, we show that the asymptotic complexity is always polynomial and of the form Θ(nk), for some integer k d, where d is the dimension of the VASS. We present a polynomial-time algorithm computing the optimal k. For general VASS, the same algorithm, which is based on a complete technique for the construction of ranking functions in VASS, produces a valid lower bound, i.e., a k such that the termination complexity is (nk). Our results are based on new insights into the geometry of VASS dynamics, which hold the potential for further applicability to VASS analysis.}, author = {Brázdil, Tomáš and Chatterjee, Krishnendu and Kučera, Antonín and Novotny, Petr and Velan, Dominik and Zuleger, Florian}, isbn = {978-1-4503-5583-4}, location = {Oxford, United Kingdom}, pages = {185 -- 194}, publisher = {IEEE}, title = {{Efficient algorithms for asymptotic bounds on termination time in VASS}}, doi = {10.1145/3209108.3209191}, volume = {F138033}, year = {2018}, } @article{157, abstract = {Social dilemmas occur when incentives for individuals are misaligned with group interests 1-7 . According to the 'tragedy of the commons', these misalignments can lead to overexploitation and collapse of public resources. The resulting behaviours can be analysed with the tools of game theory 8 . The theory of direct reciprocity 9-15 suggests that repeated interactions can alleviate such dilemmas, but previous work has assumed that the public resource remains constant over time. Here we introduce the idea that the public resource is instead changeable and depends on the strategic choices of individuals. An intuitive scenario is that cooperation increases the public resource, whereas defection decreases it. Thus, cooperation allows the possibility of playing a more valuable game with higher payoffs, whereas defection leads to a less valuable game. We analyse this idea using the theory of stochastic games 16-19 and evolutionary game theory. We find that the dependence of the public resource on previous interactions can greatly enhance the propensity for cooperation. For these results, the interaction between reciprocity and payoff feedback is crucial: neither repeated interactions in a constant environment nor single interactions in a changing environment yield similar cooperation rates. Our framework shows which feedbacks between exploitation and environment - either naturally occurring or designed - help to overcome social dilemmas.}, author = {Hilbe, Christian and Šimsa, Štepán and Chatterjee, Krishnendu and Nowak, Martin}, journal = {Nature}, number = {7713}, pages = {246 -- 249}, publisher = {Nature Publishing Group}, title = {{Evolution of cooperation in stochastic games}}, doi = {10.1038/s41586-018-0277-x}, volume = {559}, year = {2018}, } @article{454, abstract = {Direct reciprocity is a mechanism for cooperation among humans. Many of our daily interactions are repeated. We interact repeatedly with our family, friends, colleagues, members of the local and even global community. In the theory of repeated games, it is a tacit assumption that the various games that a person plays simultaneously have no effect on each other. Here we introduce a general framework that allows us to analyze “crosstalk” between a player’s concurrent games. In the presence of crosstalk, the action a person experiences in one game can alter the person’s decision in another. We find that crosstalk impedes the maintenance of cooperation and requires stronger levels of forgiveness. The magnitude of the effect depends on the population structure. In more densely connected social groups, crosstalk has a stronger effect. A harsh retaliator, such as Tit-for-Tat, is unable to counteract crosstalk. The crosstalk framework provides a unified interpretation of direct and upstream reciprocity in the context of repeated games.}, author = {Reiter, Johannes and Hilbe, Christian and Rand, David and Chatterjee, Krishnendu and Nowak, Martin}, journal = {Nature Communications}, number = {1}, publisher = {Nature Publishing Group}, title = {{Crosstalk in concurrent repeated games impedes direct reciprocity and requires stronger levels of forgiveness}}, doi = {10.1038/s41467-017-02721-8}, volume = {9}, year = {2018}, } @inproceedings{5679, abstract = {We study the almost-sure termination problem for probabilistic programs. First, we show that supermartingales with lower bounds on conditional absolute difference provide a sound approach for the almost-sure termination problem. Moreover, using this approach we can obtain explicit optimal bounds on tail probabilities of non-termination within a given number of steps. Second, we present a new approach based on Central Limit Theorem for the almost-sure termination problem, and show that this approach can establish almost-sure termination of programs which none of the existing approaches can handle. Finally, we discuss algorithmic approaches for the two above methods that lead to automated analysis techniques for almost-sure termination of probabilistic programs.}, author = {Huang, Mingzhang and Fu, Hongfei and Chatterjee, Krishnendu}, editor = {Ryu, Sukyoung}, isbn = {9783030027674}, issn = {0302-9743}, location = {Wellington, New Zealand}, pages = {181--201}, publisher = {Springer}, title = {{New approaches for almost-sure termination of probabilistic programs}}, doi = {10.1007/978-3-030-02768-1_11}, volume = {11275}, year = {2018}, } @article{5751, abstract = {Because of the intrinsic randomness of the evolutionary process, a mutant with a fitness advantage has some chance to be selected but no certainty. Any experiment that searches for advantageous mutants will lose many of them due to random drift. It is therefore of great interest to find population structures that improve the odds of advantageous mutants. Such structures are called amplifiers of natural selection: they increase the probability that advantageous mutants are selected. Arbitrarily strong amplifiers guarantee the selection of advantageous mutants, even for very small fitness advantage. Despite intensive research over the past decade, arbitrarily strong amplifiers have remained rare. Here we show how to construct a large variety of them. Our amplifiers are so simple that they could be useful in biotechnology, when optimizing biological molecules, or as a diagnostic tool, when searching for faster dividing cells or viruses. They could also occur in natural population structures.}, author = {Pavlogiannis, Andreas and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin A.}, issn = {2399-3642}, journal = {Communications Biology}, number = {1}, publisher = {Springer Nature}, title = {{Construction of arbitrarily strong amplifiers of natural selection using evolutionary graph theory}}, doi = {10.1038/s42003-018-0078-7}, volume = {1}, year = {2018}, } @inbook{59, abstract = {Graph-based games are an important tool in computer science. They have applications in synthesis, verification, refinement, and far beyond. We review graphbased games with objectives on infinite plays. We give definitions and algorithms to solve the games and to give a winning strategy. The objectives we consider are mostly Boolean, but we also look at quantitative graph-based games and their objectives. Synthesis aims to turn temporal logic specifications into correct reactive systems. We explain the reduction of synthesis to graph-based games (or equivalently tree automata) using synthesis of LTL specifications as an example. We treat the classical approach that uses determinization of parity automata and more modern approaches.}, author = {Bloem, Roderick and Chatterjee, Krishnendu and Jobstmann, Barbara}, booktitle = {Handbook of Model Checking}, editor = {Henzinger, Thomas A and Clarke, Edmund M. and Veith, Helmut and Bloem, Roderick}, isbn = {978-3-319-10574-1}, pages = {921 -- 962}, publisher = {Springer}, title = {{Graph games and reactive synthesis}}, doi = {10.1007/978-3-319-10575-8_27}, year = {2018}, } @inproceedings{5967, abstract = {The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage. Blackwell and Ferguson (1968) give an ε-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless. We prove that there is such a strategy that is ε-optimal. In fact, we show that just two states of memory are sufficient. }, author = {Hansen, Kristoffer Arnsfelt and Ibsen-Jensen, Rasmus and Neyman, Abraham}, booktitle = {Proceedings of the 2018 ACM Conference on Economics and Computation - EC '18}, isbn = {9781450358293}, location = {Ithaca, NY, United States}, pages = {149--150}, publisher = {ACM}, title = {{The Big Match with a clock and a bit of memory}}, doi = {10.1145/3219166.3219198}, year = {2018}, } @article{5993, abstract = {In this article, we consider the termination problem of probabilistic programs with real-valued variables. Thequestions concerned are: qualitative ones that ask (i) whether the program terminates with probability 1(almost-sure termination) and (ii) whether the expected termination time is finite (finite termination); andquantitative ones that ask (i) to approximate the expected termination time (expectation problem) and (ii) tocompute a boundBsuch that the probability not to terminate afterBsteps decreases exponentially (con-centration problem). To solve these questions, we utilize the notion of ranking supermartingales, which isa powerful approach for proving termination of probabilistic programs. In detail, we focus on algorithmicsynthesis of linear ranking-supermartingales over affine probabilistic programs (Apps) with both angelic anddemonic non-determinism. An important subclass of Apps is LRApp which is defined as the class of all Appsover which a linear ranking-supermartingale exists.Our main contributions are as follows. Firstly, we show that the membership problem of LRApp (i) canbe decided in polynomial time for Apps with at most demonic non-determinism, and (ii) isNP-hard and inPSPACEfor Apps with angelic non-determinism. Moreover, theNP-hardness result holds already for Appswithout probability and demonic non-determinism. Secondly, we show that the concentration problem overLRApp can be solved in the same complexity as for the membership problem of LRApp. Finally, we show thatthe expectation problem over LRApp can be solved in2EXPTIMEand isPSPACE-hard even for Apps withoutprobability and non-determinism (i.e., deterministic programs). Our experimental results demonstrate theeffectiveness of our approach to answer the qualitative and quantitative questions over Apps with at mostdemonic non-determinism.}, author = {Chatterjee, Krishnendu and Fu, Hongfei and Novotný, Petr and Hasheminezhad, Rouzbeh}, issn = {0164-0925}, journal = {ACM Transactions on Programming Languages and Systems}, number = {2}, publisher = {Association for Computing Machinery}, title = {{Algorithmic analysis of qualitative and quantitative termination problems for affine probabilistic programs}}, doi = {10.1145/3174800}, volume = {40}, year = {2018}, } @article{10417, abstract = {We present a new dynamic partial-order reduction method for stateless model checking of concurrent programs. A common approach for exploring program behaviors relies on enumerating the traces of the program, without storing the visited states (aka stateless exploration). As the number of distinct traces grows exponentially, dynamic partial-order reduction (DPOR) techniques have been successfully used to partition the space of traces into equivalence classes (Mazurkiewicz partitioning), with the goal of exploring only few representative traces from each class. We introduce a new equivalence on traces under sequential consistency semantics, which we call the observation equivalence. Two traces are observationally equivalent if every read event observes the same write event in both traces. While the traditional Mazurkiewicz equivalence is control-centric, our new definition is data-centric. We show that our observation equivalence is coarser than the Mazurkiewicz equivalence, and in many cases even exponentially coarser. We devise a DPOR exploration of the trace space, called data-centric DPOR, based on the observation equivalence.}, author = {Chalupa, Marek and Chatterjee, Krishnendu and Pavlogiannis, Andreas and Sinha, Nishant and Vaidya, Kapil}, issn = {2475-1421}, journal = {Proceedings of the ACM on Programming Languages}, location = {Los Angeles, CA, United States}, number = {POPL}, publisher = {Association for Computing Machinery}, title = {{Data-centric dynamic partial order reduction}}, doi = {10.1145/3158119}, volume = {2}, year = {2018}, } @inproceedings{79, abstract = {Markov Decision Processes (MDPs) are a popular class of models suitable for solving control decision problems in probabilistic reactive systems. We consider parametric MDPs (pMDPs) that include parameters in some of the transition probabilities to account for stochastic uncertainties of the environment such as noise or input disturbances. We study pMDPs with reachability objectives where the parameter values are unknown and impossible to measure directly during execution, but there is a probability distribution known over the parameter values. We study for the first time computing parameter-independent strategies that are expectation optimal, i.e., optimize the expected reachability probability under the probability distribution over the parameters. We present an encoding of our problem to partially observable MDPs (POMDPs), i.e., a reduction of our problem to computing optimal strategies in POMDPs. We evaluate our method experimentally on several benchmarks: a motivating (repeated) learner model; a series of benchmarks of varying configurations of a robot moving on a grid; and a consensus protocol.}, author = {Arming, Sebastian and Bartocci, Ezio and Chatterjee, Krishnendu and Katoen, Joost P and Sokolova, Ana}, location = {Beijing, China}, pages = {53--70}, publisher = {Springer}, title = {{Parameter-independent strategies for pMDPs via POMDPs}}, doi = {10.1007/978-3-319-99154-2_4}, volume = {11024}, year = {2018}, } @inbook{86, abstract = {Responsiveness—the requirement that every request to a system be eventually handled—is one of the fundamental liveness properties of a reactive system. Average response time is a quantitative measure for the responsiveness requirement used commonly in performance evaluation. We show how average response time can be computed on state-transition graphs, on Markov chains, and on game graphs. In all three cases, we give polynomial-time algorithms.}, author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan}, booktitle = {Principles of Modeling}, editor = {Lohstroh, Marten and Derler, Patricia and Sirjani, Marjan}, pages = {143 -- 161}, publisher = {Springer}, title = {{Computing average response time}}, doi = {10.1007/978-3-319-95246-8_9}, volume = {10760}, year = {2018}, } @article{738, abstract = {This paper is devoted to automatic competitive analysis of real-time scheduling algorithms for firm-deadline tasksets, where only completed tasks con- tribute some utility to the system. Given such a taskset T , the competitive ratio of an on-line scheduling algorithm A for T is the worst-case utility ratio of A over the utility achieved by a clairvoyant algorithm. We leverage the theory of quantitative graph games to address the competitive analysis and competitive synthesis problems. For the competitive analysis case, given any taskset T and any finite-memory on- line scheduling algorithm A , we show that the competitive ratio of A in T can be computed in polynomial time in the size of the state space of A . Our approach is flexible as it also provides ways to model meaningful constraints on the released task sequences that determine the competitive ratio. We provide an experimental study of many well-known on-line scheduling algorithms, which demonstrates the feasibility of our competitive analysis approach that effectively replaces human ingenuity (required Preliminary versions of this paper have appeared in Chatterjee et al. ( 2013 , 2014 ). B Andreas Pavlogiannis pavlogiannis@ist.ac.at Krishnendu Chatterjee krish.chat@ist.ac.at Alexander Kößler koe@ecs.tuwien.ac.at Ulrich Schmid s@ecs.tuwien.ac.at 1 IST Austria (Institute of Science and Technology Austria), Am Campus 1, 3400 Klosterneuburg, Austria 2 Embedded Computing Systems Group, Vienna University of Technology, Treitlstrasse 3, 1040 Vienna, Austria 123 Real-Time Syst for finding worst-case scenarios) by computing power. For the competitive synthesis case, we are just given a taskset T , and the goal is to automatically synthesize an opti- mal on-line scheduling algorithm A , i.e., one that guarantees the largest competitive ratio possible for T . We show how the competitive synthesis problem can be reduced to a two-player graph game with partial information, and establish that the compu- tational complexity of solving this game is Np -complete. The competitive synthesis problem is hence in Np in the size of the state space of the non-deterministic labeled transition system encoding the taskset. Overall, the proposed framework assists in the selection of suitable scheduling algorithms for a given taskset, which is in fact the most common situation in real-time systems design. }, author = {Chatterjee, Krishnendu and Pavlogiannis, Andreas and Kößler, Alexander and Schmid, Ulrich}, journal = {Real-Time Systems}, number = {1}, pages = {166 -- 207}, publisher = {Springer}, title = {{Automated competitive analysis of real time scheduling with graph games}}, doi = {10.1007/s11241-017-9293-4}, volume = {54}, year = {2018}, } @inproceedings{310, abstract = {A model of computation that is widely used in the formal analysis of reactive systems is symbolic algorithms. In this model the access to the input graph is restricted to consist of symbolic operations, which are expensive in comparison to the standard RAM operations. We give lower bounds on the number of symbolic operations for basic graph problems such as the computation of the strongly connected components and of the approximate diameter as well as for fundamental problems in model checking such as safety, liveness, and coliveness. Our lower bounds are linear in the number of vertices of the graph, even for constant-diameter graphs. For none of these problems lower bounds on the number of symbolic operations were known before. The lower bounds show an interesting separation of these problems from the reachability problem, which can be solved with O(D) symbolic operations, where D is the diameter of the graph. Additionally we present an approximation algorithm for the graph diameter which requires Õ(n/D) symbolic steps to achieve a (1 +ϵ)-approximation for any constant > 0. This compares to O(n/D) symbolic steps for the (naive) exact algorithm and O(D) symbolic steps for a 2-approximation. Finally we also give a refined analysis of the strongly connected components algorithms of [15], showing that it uses an optimal number of symbolic steps that is proportional to the sum of the diameters of the strongly connected components.}, author = {Chatterjee, Krishnendu and Dvorák, Wolfgang and Henzinger, Monika H and Loitzenbauer, Veronika}, location = {New Orleans, Louisiana, United States}, pages = {2341 -- 2356}, publisher = {ACM}, title = {{Lower bounds for symbolic computation on graphs: Strongly connected components, liveness, safety, and diameter}}, doi = {10.1137/1.9781611975031.151}, year = {2018}, } @inproceedings{325, abstract = {Probabilistic programs extend classical imperative programs with real-valued random variables and random branching. The most basic liveness property for such programs is the termination property. The qualitative (aka almost-sure) termination problem asks whether a given program program terminates with probability 1. While ranking functions provide a sound and complete method for non-probabilistic programs, the extension of them to probabilistic programs is achieved via ranking supermartingales (RSMs). Although deep theoretical results have been established about RSMs, their application to probabilistic programs with nondeterminism has been limited only to programs of restricted control-flow structure. For non-probabilistic programs, lexicographic ranking functions provide a compositional and practical approach for termination analysis of real-world programs. In this work we introduce lexicographic RSMs and show that they present a sound method for almost-sure termination of probabilistic programs with nondeterminism. We show that lexicographic RSMs provide a tool for compositional reasoning about almost-sure termination, and for probabilistic programs with linear arithmetic they can be synthesized efficiently (in polynomial time). We also show that with additional restrictions even asymptotic bounds on expected termination time can be obtained through lexicographic RSMs. Finally, we present experimental results on benchmarks adapted from previous work to demonstrate the effectiveness of our approach.}, author = {Agrawal, Sheshansh and Chatterjee, Krishnendu and Novotny, Petr}, location = {Los Angeles, CA, USA}, number = {POPL}, publisher = {ACM}, title = {{Lexicographic ranking supermartingales: an efficient approach to termination of probabilistic programs}}, doi = {10.1145/3158122}, volume = {2}, year = {2018}, } @article{419, abstract = {Reciprocity is a major factor in human social life and accounts for a large part of cooperation in our communities. Direct reciprocity arises when repeated interactions occur between the same individuals. The framework of iterated games formalizes this phenomenon. Despite being introduced more than five decades ago, the concept keeps offering beautiful surprises. Recent theoretical research driven by new mathematical tools has proposed a remarkable dichotomy among the crucial strategies: successful individuals either act as partners or as rivals. Rivals strive for unilateral advantages by applying selfish or extortionate strategies. Partners aim to share the payoff for mutual cooperation, but are ready to fight back when being exploited. Which of these behaviours evolves depends on the environment. Whereas small population sizes and a limited number of rounds favour rivalry, partner strategies are selected when populations are large and relationships stable. Only partners allow for evolution of cooperation, while the rivals’ attempt to put themselves first leads to defection. Hilbe et al. synthesize recent theoretical work on zero-determinant and ‘rival’ versus ‘partner’ strategies in social dilemmas. They describe the environments under which these contrasting selfish or cooperative strategies emerge in evolution.}, author = {Hilbe, Christian and Chatterjee, Krishnendu and Nowak, Martin}, journal = {Nature Human Behaviour}, pages = {469–477}, publisher = {Nature Publishing Group}, title = {{Partners and rivals in direct reciprocity}}, doi = {10.1038/s41562-018-0320-9}, volume = {2}, year = {2018}, } @inproceedings{34, abstract = {Partially observable Markov decision processes (POMDPs) are widely used in probabilistic planning problems in which an agent interacts with an environment using noisy and imprecise sensors. We study a setting in which the sensors are only partially defined and the goal is to synthesize “weakest” additional sensors, such that in the resulting POMDP, there is a small-memory policy for the agent that almost-surely (with probability 1) satisfies a reachability objective. We show that the problem is NP-complete, and present a symbolic algorithm by encoding the problem into SAT instances. We illustrate trade-offs between the amount of memory of the policy and the number of additional sensors on a simple example. We have implemented our approach and consider three classical POMDP examples from the literature, and show that in all the examples the number of sensors can be significantly decreased (as compared to the existing solutions in the literature) without increasing the complexity of the policies.}, author = {Chatterjee, Krishnendu and Chemlík, Martin and Topcu, Ufuk}, booktitle = {28th International Conference on Automated Planning and Scheduling}, location = {Delft, Netherlands}, pages = {47 -- 55}, publisher = {AAAI Press}, title = {{Sensor synthesis for POMDPs with reachability objectives}}, doi = {10.1609/icaps.v28i1.13875}, volume = {2018}, year = {2018}, } @inproceedings{35, abstract = {We consider planning problems for graphs, Markov decision processes (MDPs), and games on graphs. While graphs represent the most basic planning model, MDPs represent interaction with nature and games on graphs represent interaction with an adversarial environment. We consider two planning problems where there are k different target sets, and the problems are as follows: (a) the coverage problem asks whether there is a plan for each individual target set; and (b) the sequential target reachability problem asks whether the targets can be reached in sequence. For the coverage problem, we present a linear-time algorithm for graphs, and quadratic conditional lower bound for MDPs and games on graphs. For the sequential target problem, we present a linear-time algorithm for graphs, a sub-quadratic algorithm for MDPs, and a quadratic conditional lower bound for games on graphs. Our results with conditional lower bounds establish (i) model-separation results showing that for the coverage problem MDPs and games on graphs are harder than graphs and for the sequential reachability problem games on graphs are harder than MDPs and graphs; and (ii) objective-separation results showing that for MDPs the coverage problem is harder than the sequential target problem.}, author = {Chatterjee, Krishnendu and Dvorák, Wolfgang and Henzinger, Monika H and Svozil, Alexander}, booktitle = {28th International Conference on Automated Planning and Scheduling}, location = {Delft, Netherlands}, publisher = {AAAI Press}, title = {{Algorithms and conditional lower bounds for planning problems}}, year = {2018}, } @article{198, abstract = {We consider a class of students learning a language from a teacher. The situation can be interpreted as a group of child learners receiving input from the linguistic environment. The teacher provides sample sentences. The students try to learn the grammar from the teacher. In addition to just listening to the teacher, the students can also communicate with each other. The students hold hypotheses about the grammar and change them if they receive counter evidence. The process stops when all students have converged to the correct grammar. We study how the time to convergence depends on the structure of the classroom by introducing and evaluating various complexity measures. We find that structured communication between students, although potentially introducing confusion, can greatly reduce some of the complexity measures. Our theory can also be interpreted as applying to the scientific process, where nature is the teacher and the scientists are the students.}, author = {Ibsen-Jensen, Rasmus and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin}, issn = {1742-5662}, journal = {Journal of the Royal Society Interface}, number = {140}, publisher = {Royal Society}, title = {{Language acquisition with communication between learners}}, doi = {10.1098/rsif.2018.0073}, volume = {15}, year = {2018}, } @article{2, abstract = {Indirect reciprocity explores how humans act when their reputation is at stake, and which social norms they use to assess the actions of others. A crucial question in indirect reciprocity is which social norms can maintain stable cooperation in a society. Past research has highlighted eight such norms, called “leading-eight” strategies. This past research, however, is based on the assumption that all relevant information about other population members is publicly available and that everyone agrees on who is good or bad. Instead, here we explore the reputation dynamics when information is private and noisy. We show that under these conditions, most leading-eight strategies fail to evolve. Those leading-eight strategies that do evolve are unable to sustain full cooperation.Indirect reciprocity is a mechanism for cooperation based on shared moral systems and individual reputations. It assumes that members of a community routinely observe and assess each other and that they use this information to decide who is good or bad, and who deserves cooperation. When information is transmitted publicly, such that all community members agree on each other’s reputation, previous research has highlighted eight crucial moral systems. These “leading-eight” strategies can maintain cooperation and resist invasion by defectors. However, in real populations individuals often hold their own private views of others. Once two individuals disagree about their opinion of some third party, they may also see its subsequent actions in a different light. Their opinions may further diverge over time. Herein, we explore indirect reciprocity when information transmission is private and noisy. We find that in the presence of perception errors, most leading-eight strategies cease to be stable. Even if a leading-eight strategy evolves, cooperation rates may drop considerably when errors are common. Our research highlights the role of reliable information and synchronized reputations to maintain stable moral systems.}, author = {Hilbe, Christian and Schmid, Laura and Tkadlec, Josef and Chatterjee, Krishnendu and Nowak, Martin}, journal = {PNAS}, number = {48}, pages = {12241--12246}, publisher = {National Academy of Sciences}, title = {{Indirect reciprocity with private, noisy, and incomplete information}}, doi = {10.1073/pnas.1810565115}, volume = {115}, year = {2018}, }