34,216 research outputs found
Countdown games, and simulation on (succinct) one-counter nets
We answer an open complexity question by Hofman, Lasota, Mayr, Totzke (LMCS
2016) [HLMT16] for simulation preorder of succinct one-counter nets (i.e.,
one-counter automata with no zero tests where counter increments and decrements
are integers written in binary), by showing that all relations between
bisimulation equivalence and simulation preorder are EXPSPACE-hard for these
nets. We describe a reduction from reachability games whose
EXPSPACE-completeness in the case of succinct one-counter nets was shown by
Hunter [RP 2015], by using other results. We also provide a direct
self-contained EXPSPACE-completeness proof for a special case of such
reachability games, namely for a modification of countdown games that were
shown EXPTIME-complete by Jurdzinski, Sproston, Laroussinie [LMCS 2008]; in our
modification the initial counter value is not given but is freely chosen by the
first player. We also present a new simplified proof of the belt theorem that
gives a simple graphic presentation of simulation preorder on one-counter nets
and leads to a polynomial-space algorithm; it is an alternative to the proof
from [HLMT16].Comment: A part of this paper elaborates arxiv-paper 1801.01073 and the
related paper presented at Reachability Problems 201
Sequentiality vs. Concurrency in Games and Logic
Connections between the sequentiality/concurrency distinction and the
semantics of proofs are investigated, with particular reference to games and
Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc
Coalition structure generation in cooperative games with compact representations
This paper presents a new way of formalizing the coalition structure generation problem (CSG) so that we can apply constraint optimization techniques to it. Forming effective coalitions is a major research challenge in AI and multi-agent systems. CSG involves partitioning a set of agents into coalitions to maximize social surplus. Traditionally, the input of the CSG problem is a black-box function called a characteristic function, which takes a coalition as input and returns the value of the coalition. As a result, applying constraint optimization techniques to this problem has been infeasible. However, characteristic functions that appear in practice often can be represented concisely by a set of rules, rather than treating the function as a black box. Then we can solve the CSG problem more efficiently by directly applying constraint optimization techniques to this compact representation. We present new formalizations of the CSG problem by utilizing recently developed compact representation schemes for characteristic functions. We first characterize the complexity of CSG under these representation schemes. In this context, the complexity is driven more by the number of rules than by the number of agents. As an initial step toward developing efficient constraint optimization algorithms for solving the CSG problem, we also develop mixed integer programming formulations and show that an off-the-shelf optimization package can perform reasonably well
A Logic-Based Representation for Coalitional Games with Externalities
We consider the issue of representing coalitional games in multiagent systems that exhibit externalities from coalition formation, i.e., systems in which the gain from forming a coalition may be affected by the formation of other co-existing coalitions. Although externalities play a key role in many real-life situations, very little attention has been given to this issue in the multi-agent system literature, especially with regard to the computational aspects involved. To this end, we propose a new representation which, in the spirit of Ieong and Shoham [9], is based on Boolean expressions. The idea behind our representation is to construct much richer expressions that allow for capturing externalities induced upon coalitions. We show that the new representation is fully expressive, at least as concise as the conventional partition function game representation and, for many games, exponentially more concise. We evaluate the efficiency of our new representation by considering the problem of computing the Extended and Generalized Shapley value, a powerful extension of the conventional Shapley value to games with externalities. We show that by using our new representation, the Extended and Generalized Shapley value, which has not been studied in the computer science literature to date, can be computed in time linear in the size of the input
Wadge Degrees of -Languages of Petri Nets
We prove that -languages of (non-deterministic) Petri nets and
-languages of (non-deterministic) Turing machines have the same
topological complexity: the Borel and Wadge hierarchies of the class of
-languages of (non-deterministic) Petri nets are equal to the Borel and
Wadge hierarchies of the class of -languages of (non-deterministic)
Turing machines which also form the class of effective analytic sets. In
particular, for each non-null recursive ordinal there exist some -complete and some -complete -languages of Petri nets, and the supremum of
the set of Borel ranks of -languages of Petri nets is the ordinal
, which is strictly greater than the first non-recursive ordinal
. We also prove that there are some -complete, hence non-Borel, -languages of Petri nets, and
that it is consistent with ZFC that there exist some -languages of
Petri nets which are neither Borel nor -complete. This
answers the question of the topological complexity of -languages of
(non-deterministic) Petri nets which was left open in [DFR14,FS14].Comment: arXiv admin note: text overlap with arXiv:0712.1359, arXiv:0804.326
Estimating operator norms using covering nets
We present several polynomial- and quasipolynomial-time approximation schemes
for a large class of generalized operator norms. Special cases include the
norm of matrices for , the support function of the set of
separable quantum states, finding the least noisy output of
entanglement-breaking quantum channels, and approximating the injective tensor
norm for a map between two Banach spaces whose factorization norm through
is bounded.
These reproduce and in some cases improve upon the performance of previous
algorithms by Brand\~ao-Christandl-Yard and followup work, which were based on
the Sum-of-Squares hierarchy and whose analysis used techniques from quantum
information such as the monogamy principle of entanglement. Our algorithms, by
contrast, are based on brute force enumeration over carefully chosen covering
nets. These have the advantage of using less memory, having much simpler proofs
and giving new geometric insights into the problem. Net-based algorithms for
similar problems were also presented by Shi-Wu and Barak-Kelner-Steurer, but in
each case with a run-time that is exponential in the rank of some matrix. We
achieve polynomial or quasipolynomial runtimes by using the much smaller nets
that exist in spaces. This principle has been used in learning theory,
where it is known as Maurey's empirical method.Comment: 24 page
Learning Cooperative Games
This paper explores a PAC (probably approximately correct) learning model in
cooperative games. Specifically, we are given random samples of coalitions
and their values, taken from some unknown cooperative game; can we predict the
values of unseen coalitions? We study the PAC learnability of several
well-known classes of cooperative games, such as network flow games, threshold
task games, and induced subgraph games. We also establish a novel connection
between PAC learnability and core stability: for games that are efficiently
learnable, it is possible to find payoff divisions that are likely to be stable
using a polynomial number of samples.Comment: accepted to IJCAI 201
- …