1,150 research outputs found
Infinite-Duration Bidding Games
Two-player games on graphs are widely studied in formal methods as they model
the interaction between a system and its environment. The game is played by
moving a token throughout a graph to produce an infinite path. There are
several common modes to determine how the players move the token through the
graph; e.g., in turn-based games the players alternate turns in moving the
token. We study the {\em bidding} mode of moving the token, which, to the best
of our knowledge, has never been studied in infinite-duration games. The
following bidding rule was previously defined and called Richman bidding. Both
players have separate {\em budgets}, which sum up to . In each turn, a
bidding takes place: Both players submit bids simultaneously, where a bid is
legal if it does not exceed the available budget, and the higher bidder pays
his bid to the other player and moves the token. The central question studied
in bidding games is a necessary and sufficient initial budget for winning the
game: a {\em threshold} budget in a vertex is a value such that
if Player 's budget exceeds , he can win the game, and if Player 's
budget exceeds , he can win the game. Threshold budgets were previously
shown to exist in every vertex of a reachability game, which have an
interesting connection with {\em random-turn} games -- a sub-class of simple
stochastic games in which the player who moves is chosen randomly. We show the
existence of threshold budgets for a qualitative class of infinite-duration
games, namely parity games, and a quantitative class, namely mean-payoff games.
The key component of the proof is a quantitative solution to strongly-connected
mean-payoff bidding games in which we extend the connection with random-turn
games to these games, and construct explicit optimal strategies for both
players.Comment: A short version appeared in CONCUR 2017. The paper is accepted to
JAC
Determinacy in Discrete-Bidding Infinite-Duration Games
In two-player games on graphs, the players move a token through a graph to
produce an infinite path, which determines the winner of the game. Such games
are central in formal methods since they model the interaction between a
non-terminating system and its environment. In bidding games the players bid
for the right to move the token: in each round, the players simultaneously
submit bids, and the higher bidder moves the token and pays the other player.
Bidding games are known to have a clean and elegant mathematical structure that
relies on the ability of the players to submit arbitrarily small bids. Many
applications, however, require a fixed granularity for the bids, which can
represent, for example, the monetary value expressed in cents. We study, for
the first time, the combination of discrete-bidding and infinite-duration
games. Our most important result proves that these games form a large
determined subclass of concurrent games, where determinacy is the strong
property that there always exists exactly one player who can guarantee winning
the game. In particular, we show that, in contrast to non-discrete bidding
games, the mechanism with which tied bids are resolved plays an important role
in discrete-bidding games. We study several natural tie-breaking mechanisms and
show that, while some do not admit determinacy, most natural mechanisms imply
determinacy for every pair of initial budgets
Radical and ion molecule mechanisms in the polymerization of hydrocarbons and chlorosilanes in RF plasmas at low pressures ( 1.0 torr)
The ion-molecule and the radical-molecule mechanisms are responsible for the dissociation of hydrocarbons, and chlorosilane monomers and the formation of polymerized species, respectively, in the plasma state of a RF discharge. In the plasma, of a mixture of monomer with Ar, the rate determining step for both dissociation and polymerization is governed by an ion-molecular type interaction. Additions of H2 or NH3 to the monomer Ar(+) mixture transforms the rate determining step from an ion-molecular interaction to a radical-molecule type interaction for both monomer dissociation and polymerization processes
Homogeneous reactions of hydrocarbons, silane, and chlorosilanes in radiofrequency plasmas at low pressures
The ion-molecule and radical-molecule mechanisms are responsible for the dissociation of hydrocarbon, silane, and chlorosilane monomers and the formation of polymerized species, respectively, in an RF plasma discharge. In a plasma containing a mixture of monomer and argon the rate-determining step for both dissociation and polymerization is governed by an ion-molecule type of interaction. Adding hydrogen or ammonia to the monomer-argon mixture transforms the rate-determining step from an ion-molecule interaction to a radical-molecule interaction for both monomer dissociation and polymerization
Similarity classes of 3x3 matrices over a local principal ideal ring
In this paper similarity classes of three by three matrices over a local
principal ideal commutative ring are analyzed. When the residue field is
finite, a generating function for the number of similarity classes for all
finite quotients of the ring is computed explicitly.Comment: 14 pages, final version, to appear in Communications in Algebr
Correlations between plasma variables and the deposition process of Si films from chlorosilanes in low pressure RF plasma of argon and hydrogen
The dissociation of chlorosilanes to silicon and its deposition on a solid substrate in a RF plasma of mixtures of argon and hydrogen were investigated as a function of the macrovariables of the plasma. The dissociation mechanism of chlorosilanes and HCl as well as the formation of Si in the plasma state were studied by sampling the plasma with a quadrupole mass spectrometer. Macrovariables such as pressure, net RF power input and locations in the plasma reactor strongly influence the kinetics of dissociation. The deposition process of microcrystalline silicon films and its chlorine contamination were correlated to the dissociation mechanism of chlorosilanes and HCl
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