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 $1$. 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 $t \in [0,1]$ such that if Player $1$'s budget exceeds $t$, he can win the game, and if Player $2$'s budget exceeds $1-t$, 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