9,842 research outputs found
A Logic Programming Approach to Knowledge-State Planning: Semantics and Complexity
We propose a new declarative planning language, called K, which is based on
principles and methods of logic programming. In this language, transitions
between states of knowledge can be described, rather than transitions between
completely described states of the world, which makes the language well-suited
for planning under incomplete knowledge. Furthermore, it enables the use of
default principles in the planning process by supporting negation as failure.
Nonetheless, K also supports the representation of transitions between states
of the world (i.e., states of complete knowledge) as a special case, which
shows that the language is very flexible. As we demonstrate on particular
examples, the use of knowledge states may allow for a natural and compact
problem representation. We then provide a thorough analysis of the
computational complexity of K, and consider different planning problems,
including standard planning and secure planning (also known as conformant
planning) problems. We show that these problems have different complexities
under various restrictions, ranging from NP to NEXPTIME in the propositional
case. Our results form the theoretical basis for the DLV^K system, which
implements the language K on top of the DLV logic programming system.Comment: 48 pages, appeared as a Technical Report at KBS of the Vienna
University of Technology, see http://www.kr.tuwien.ac.at/research/reports
Push-Pull Block Puzzles are Hard
This paper proves that push-pull block puzzles in 3D are PSPACE-complete to
solve, and push-pull block puzzles in 2D with thin walls are NP-hard to solve,
settling an open question by Zubaran and Ritt. Push-pull block puzzles are a
type of recreational motion planning problem, similar to Sokoban, that involve
moving a `robot' on a square grid with obstacles. The obstacles
cannot be traversed by the robot, but some can be pushed and pulled by the
robot into adjacent squares. Thin walls prevent movement between two adjacent
squares. This work follows in a long line of algorithms and complexity work on
similar problems. The 2D push-pull block puzzle shows up in the video games
Pukoban as well as The Legend of Zelda: A Link to the Past, giving another
proof of hardness for the latter. This variant of block-pushing puzzles is of
particular interest because of its connections to reversibility, since any
action (e.g., push or pull) can be inverted by another valid action (e.g., pull
or push).Comment: Full version of CIAC 2017 paper. 17 page
Placing Arrows in Directed Graph Drawings
We consider the problem of placing arrow heads in directed graph drawings
without them overlapping other drawn objects. This gives drawings where edge
directions can be deduced unambiguously. We show hardness of the problem,
present exact and heuristic algorithms, and report on a practical study.Comment: Appears in the Proceedings of the 24th International Symposium on
Graph Drawing and Network Visualization (GD 2016
The Complexity of Reasoning with FODD and GFODD
Recent work introduced Generalized First Order Decision Diagrams (GFODD) as a
knowledge representation that is useful in mechanizing decision theoretic
planning in relational domains. GFODDs generalize function-free first order
logic and include numerical values and numerical generalizations of existential
and universal quantification. Previous work presented heuristic inference
algorithms for GFODDs and implemented these heuristics in systems for decision
theoretic planning. In this paper, we study the complexity of the computational
problems addressed by such implementations. In particular, we study the
evaluation problem, the satisfiability problem, and the equivalence problem for
GFODDs under the assumption that the size of the intended model is given with
the problem, a restriction that guarantees decidability. Our results provide a
complete characterization placing these problems within the polynomial
hierarchy. The same characterization applies to the corresponding restriction
of problems in first order logic, giving an interesting new avenue for
efficient inference when the number of objects is bounded. Our results show
that for formulas, and for corresponding GFODDs, evaluation and
satisfiability are complete, and equivalence is
complete. For formulas evaluation is complete, satisfiability
is one level higher and is complete, and equivalence is
complete.Comment: A short version of this paper appears in AAAI 2014. Version 2
includes a reorganization and some expanded proof
Answer Set Planning Under Action Costs
Recently, planning based on answer set programming has been proposed as an
approach towards realizing declarative planning systems. In this paper, we
present the language Kc, which extends the declarative planning language K by
action costs. Kc provides the notion of admissible and optimal plans, which are
plans whose overall action costs are within a given limit resp. minimum over
all plans (i.e., cheapest plans). As we demonstrate, this novel language allows
for expressing some nontrivial planning tasks in a declarative way.
Furthermore, it can be utilized for representing planning problems under other
optimality criteria, such as computing ``shortest'' plans (with the least
number of steps), and refinement combinations of cheapest and fastest plans. We
study complexity aspects of the language Kc and provide a transformation to
logic programs, such that planning problems are solved via answer set
programming. Furthermore, we report experimental results on selected problems.
Our experience is encouraging that answer set planning may be a valuable
approach to expressive planning systems in which intricate planning problems
can be naturally specified and solved
Complexity of Determining Nonemptiness of the Core
Coalition formation is a key problem in automated negotiation among
self-interested agents, and other multiagent applications. A coalition of
agents can sometimes accomplish things that the individual agents cannot, or
can do things more efficiently. However, motivating the agents to abide to a
solution requires careful analysis: only some of the solutions are stable in
the sense that no group of agents is motivated to break off and form a new
coalition. This constraint has been studied extensively in cooperative game
theory. However, the computational questions around this constraint have
received less attention. When it comes to coalition formation among software
agents (that represent real-world parties), these questions become increasingly
explicit.
In this paper we define a concise general representation for games in
characteristic form that relies on superadditivity, and show that it allows for
efficient checking of whether a given outcome is in the core. We then show that
determining whether the core is nonempty is -complete both with
and without transferable utility. We demonstrate that what makes the problem
hard in both cases is determining the collaborative possibilities (the set of
outcomes possible for the grand coalition), by showing that if these are given,
the problem becomes tractable in both cases. However, we then demonstrate that
for a hybrid version of the problem, where utility transfer is possible only
within the grand coalition, the problem remains -complete even
when the collaborative possibilities are given
Trains, Games, and Complexity: 0/1/2-Player Motion Planning through Input/Output Gadgets
We analyze the computational complexity of motion planning through local
"input/output" gadgets with separate entrances and exits, and a subset of
allowed traversals from entrances to exits, each of which changes the state of
the gadget and thereby the allowed traversals. We study such gadgets in the 0-,
1-, and 2-player settings, in particular extending past
motion-planning-through-gadgets work to 0-player games for the first time, by
considering "branchless" connections between gadgets that route every gadget's
exit to a unique gadget's entrance. Our complexity results include containment
in L, NL, P, NP, and PSPACE; as well as hardness for NL, P, NP, and PSPACE. We
apply these results to show PSPACE-completeness for certain mechanics in
Factorio, [the Sequence], and a restricted version of Trainyard, improving
prior results. This work strengthens prior results on switching graphs and
reachability switching games.Comment: 37 pages, 36 figure
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