Qualitative Analysis of Concurrent Mean-payoff Games

We consider concurrent games played by two-players on a finite-state graph, where in every round the players simultaneously choose a move, and the current state along with the joint moves determine the successor state. We study a fundamental objective, namely, mean-payoff objective, where a reward is associated to each transition, and the goal of player 1 is to maximize the long-run average of the rewards, and the objective of player 2 is strictly the opposite. The path constraint for player 1 could be qualitative, i.e., the mean-payoff is the maximal reward, or arbitrarily close to it; or quantitative, i.e., a given threshold between the minimal and maximal reward. We consider the computation of the almost-sure (resp. positive) winning sets, where player 1 can ensure that the path constraint is satisfied with probability 1 (resp. positive probability). Our main results for qualitative path constraints are as follows: (1) we establish qualitative determinacy results that show that for every state either player 1 has a strategy to ensure almost-sure (resp. positive) winning against all player-2 strategies, or player 2 has a spoiling strategy to falsify almost-sure (resp. positive) winning against all player-1 strategies; (2) we present optimal strategy complexity results that precisely characterize the classes of strategies required for almost-sure and positive winning for both players; and (3) we present quadratic time algorithms to compute the almost-sure and the positive winning sets, matching the best known bound of algorithms for much simpler problems (such as reachability objectives). For quantitative constraints we show that a polynomial time solution for the almost-sure or the positive winning set would imply a solution to a long-standing open problem (the value problem for turn-based deterministic mean-payoff games) that is not known to be solvable in polynomial time

Fair task allocation in transportation

Task allocation problems have traditionally focused on cost optimization. However, more and more attention is being given to cases in which cost should not always be the sole or major consideration. In this paper we study a fair task allocation problem in transportation where an optimal allocation not only has low cost but more importantly, it distributes tasks as even as possible among heterogeneous participants who have different capacities and costs to execute tasks. To tackle this fair minimum cost allocation problem we analyze and solve it in two parts using two novel polynomial-time algorithms. We show that despite the new fairness criterion, the proposed algorithms can solve the fair minimum cost allocation problem optimally in polynomial time. In addition, we conduct an extensive set of experiments to investigate the trade-off between cost minimization and fairness. Our experimental results demonstrate the benefit of factoring fairness into task allocation. Among the majority of test instances, fairness comes with a very small price in terms of cost

Fragments of ML Decidable by Nested Data Class Memory Automata

The call-by-value language RML may be viewed as a canonical restriction of Standard ML to ground-type references, augmented by a "bad variable" construct in the sense of Reynolds. We consider the fragment of (finitary) RML terms of order at most 1 with free variables of order at most 2, and identify two subfragments of this for which we show observational equivalence to be decidable. The first subfragment consists of those terms in which the P-pointers in the game semantic representation are determined by the underlying sequence of moves. The second subfragment consists of terms in which the O-pointers of moves corresponding to free variables in the game semantic representation are determined by the underlying moves. These results are shown using a reduction to a form of automata over data words in which the data values have a tree-structure, reflecting the tree-structure of the threads in the game semantic plays. In addition we show that observational equivalence is undecidable at every third- or higher-order type, every second-order type which takes at least two first-order arguments, and every second-order type (of arity greater than one) that has a first-order argument which is not the final argument

On approximate decidability of minimal programs

An index $e$ in a numbering of partial-recursive functions is called minimal if every lesser index computes a different function from $e$. Since the 1960's it has been known that, in any reasonable programming language, no effective procedure determines whether or not a given index is minimal. We investigate whether the task of determining minimal indices can be solved in an approximate sense. Our first question, regarding the set of minimal indices, is whether there exists an algorithm which can correctly label 1 out of $k$ indices as either minimal or non-minimal. Our second question, regarding the function which computes minimal indices, is whether one can compute a short list of candidate indices which includes a minimal index for a given program. We give some negative results and leave the possibility of positive results as open questions

Stochastic models for biological evolution

In this work, we deal with the problem of creating a model that describes a population of agents undergoing Darwinian Evolution, which takes into account the basic phenomena of this process. According to the principles of evolutionary biology, Evolution occurs if there is selection and adaptation of phenotypes, mutation of genotypes, presence of physical space. The evolution of a biological population is then described by a system of ordinary stochastic differential equations; the basic model of dynamics represents the trend of a population divided into different types, with relative frequency in a simplex. The law governing this dynamics is called Replicator Dynamics: the growth rate of type k is measured in terms of evolutionary advantage, with its own fitness compared to the average in the population. The replicator dynamics model turns into a stochastic process when we consider random mutations that can transform fractions of individuals into others. The two main forces of Evolution, selection and mutation, act on different layers: the environment acts on the phenotype, selecting the fittest, while the randomness of the mutations affects the genotype. This difference is underlined in the model, where each genotype express a phenotype, and fitness influences emerging traits, not explicitly encoded in genotypes. The presence of a potentially infinite space of available genomes makes sure that variants of individuals with characteristics never seen before can be generated. In conclusion, numerical simulations are provided for some applications of the model, such as a variation of Conway's Game of Lif

A scalable dynamic parking allocation framework

International audienceCities suffer from high traffic c ongestion of which one of the main causes is the unorganized pursuit for available parking. Apart from traffic congestion, the blind search for a parking slot causes financial and environmental losses. We consider a general parking allocation scenario in which the GPS data of a set of vehicles, such as the current locations and destinations of the vehicles, are available to a central agency which will guide the vehicles toward a designated parking lot, instead of the entered destination. In its natural form, the parking allocation problem is dynamic, i.e., its input is continuously updated. Therefore, standard static allocation and assignment rules do not apply in this case. In this paper, we propose a framework capable of tackling these real-time updates. From a methodological point of view, solving the dynamic version of the parking allocation problem represents a quantum leap compared with solving the static version. We achieve this goal by solving a sequence of 0-1 programming models over the planning horizon, and we develop several parking policies. The proposed policies are empirically compared on real data gathered from three European cities: Belgrade, Luxembourg, and Lyon. The results show that our framework is scalable and can improve the quality of the allocation, in particular when parking capacities are low

Improved Algorithms for Parity and Streett objectives

The computation of the winning set for parity objectives and for Streett objectives in graphs as well as in game graphs are central problems in computer-aided verification, with application to the verification of closed systems with strong fairness conditions, the verification of open systems, checking interface compatibility, well-formedness of specifications, and the synthesis of reactive systems. We show how to compute the winning set on $n$ vertices for (1) parity-3 (aka one-pair Streett) objectives in game graphs in time $O(n^{5/2})$ and for (2) k-pair Streett objectives in graphs in time $O(n^2 + nk \log n)$. For both problems this gives faster algorithms for dense graphs and represents the first improvement in asymptotic running time in 15 years