27 research outputs found
On the Treewidth of Hanoi Graphs
The objective of the well-known Towers of Hanoi puzzle is to move a set of disks one at a time from one of a set of pegs to another, while keeping the disks sorted on each peg. We propose an adversarial variation in which the first player forbids a set of states in the puzzle, and the second player must then convert one randomly-selected state to another without passing through forbidden states. Analyzing this version raises the question of the treewidth of Hanoi graphs. We find this number exactly for three-peg puzzles and provide nearly-tight asymptotic bounds for larger numbers of pegs
Benchmarks for Parity Games (extended version)
We propose a benchmark suite for parity games that includes all benchmarks
that have been used in the literature, and make it available online. We give an
overview of the parity games, including a description of how they have been
generated. We also describe structural properties of parity games, and using
these properties we show that our benchmarks are representative. With this work
we provide a starting point for further experimentation with parity games.Comment: The corresponding tool and benchmarks are available from
https://github.com/jkeiren/paritygame-generator. This is an extended version
of the paper that has been accepted for FSEN 201
IASCAR: Incremental Answer Set Counting by Anytime Refinement
Answer set programming (ASP) is a popular declarative programming paradigm
with various applications. Programs can easily have many answer sets that
cannot be enumerated in practice, but counting still allows quantifying
solution spaces. If one counts under assumptions on literals, one obtains a
tool to comprehend parts of the solution space, so-called answer set
navigation. However, navigating through parts of the solution space requires
counting many times, which is expensive in theory. Knowledge compilation
compiles instances into representations on which counting works in polynomial
time. However, these techniques exist only for CNF formulas, and compiling ASP
programs into CNF formulas can introduce an exponential overhead. This paper
introduces a technique to iteratively count answer sets under assumptions on
knowledge compilations of CNFs that encode supported models. Our anytime
technique uses the inclusion-exclusion principle to improve bounds by over- and
undercounting systematically. In a preliminary empirical analysis, we
demonstrate promising results. After compiling the input (offline phase), our
approach quickly (re)counts.Comment: Under consideration in Theory and Practice of Logic Programming
(TPLP