298 research outputs found
Quantified Boolean Formula Games and Their Complexities
Consider QBF, the Quantified Boolean Formula problem, as a combinatorial game
ruleset. The problem is rephrased as determining the winner of the game where
two opposing players take turns assigning values to boolean variables. In this
paper, three common variations of games are applied to create seven new games:
whether each player is restricted to where they may play, which values they may
set variables to, or the condition they are shooting for at the end of the
game. The complexity for determining which player can win is analyzed for all
games. Of the seven, two are trivially in P and the other five are
PSPACE-complete. These varying properties are common for combinatorial games;
reductions from these five hard games can simplify the process for showing the
PSPACE-hardness of other games.Comment: 14 pages, 0 figures, for Integers 2013 Conference proceeding
Impartial coloring games
Coloring games are combinatorial games where the players alternate painting
uncolored vertices of a graph one of colors. Each different ruleset
specifies that game's coloring constraints. This paper investigates six
impartial rulesets (five new), derived from previously-studied graph coloring
schemes, including proper map coloring, oriented coloring, 2-distance coloring,
weak coloring, and sequential coloring. For each, we study the outcome classes
for special cases and general computational complexity. In some cases we pay
special attention to the Grundy function
Parameterized Linear Temporal Logics Meet Costs: Still not Costlier than LTL
We continue the investigation of parameterized extensions of Linear Temporal
Logic (LTL) that retain the attractive algorithmic properties of LTL: a
polynomial space model checking algorithm and a doubly-exponential time
algorithm for solving games. Alur et al. and Kupferman et al. showed that this
is the case for Parametric LTL (PLTL) and PROMPT-LTL respectively, which have
temporal operators equipped with variables that bound their scope in time.
Later, this was also shown to be true for Parametric LDL (PLDL), which extends
PLTL to be able to express all omega-regular properties.
Here, we generalize PLTL to systems with costs, i.e., we do not bound the
scope of operators in time, but bound the scope in terms of the cost
accumulated during time. Again, we show that model checking and solving games
for specifications in PLTL with costs is not harder than the corresponding
problems for LTL. Finally, we discuss PLDL with costs and extensions to
multiple cost functions.Comment: In Proceedings GandALF 2015, arXiv:1509.0685
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