Complexity results for standard benchmark domains in planning

The use of computational complexity in planning, and in AI in general, has always been a disputed topic. A major problem with ordinary worst-case analyses is that they do not provide any quantitative information: they do not tell us much about the running time of concrete algorithms, nor do they tell us much about the running time of optimal algorithms. We address problems like this by presenting results based on the exponential time hypothesis (ETH), which is a widely accepted hypothesis concerning the time complexity of 3-SAT. By using this approach, we provide, for instance, almost matching upper and lower bounds onthe time complexity of propositional planning.

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“…An excellent starting point is the article by Helmert [13]. Let us consider the benchmark problem GRID for instance.…”

Section: Theorem 11 Pe( Psn) Takes Time (2 ||P || 1/3 ) To Solve Unlmentioning

confidence: 99%

Refining complexity analyses in planning by exploiting the exponential time hypothesis

Aghighi

Bäckström

Jönsson

et al. 2016

Ann Math Artif Intell

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“…Recently, there is increasing interest and progress in AI systems that behave well in a more general range of situations. The evaluation procedures, benchmarks and computations are hence very different, depending on whether we focus on specialised benchmarks [72,38,24,116] or on more general problems [96,31,94]. Despite this trend, AI is still lacking general, well-grounded and universally accepted intelligence measurement tools.…”

Section: Introductionmentioning

confidence: 99%

Towards a Universal Test of Social Intelligence

Cabrera¹

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Under the view of artificial intelligence, an intelligent agent is an autonomous entity which interacts in an environment through observations and actions, trying to achieve one or more goals with the aid of several signals called rewards. The creation of intelligent agents is proliferating during the last decades, and the evaluation of their intelligence is a fundamental issue for their understanding, construction and improvement.Social intelligence is recently obtaining special attention in the creation of intelligent agents due to the current view of human intelligence as highly social. Social intelligence in natural and artificial systems is usually measured by the evaluation of associated traits or tasks that are deemed to represent some facets of social behaviour. The amalgamation of these traits or tasks is then used to configure an operative notion of social intelligence. However, this operative notion does not truly represent what social intelligence is and a definition following this principle will not be precise. Instead, in this thesis we investigate the evaluation of social intelligence in a more formal and general way, by actually considering the evaluee's interaction with other agents.In this thesis we analyse the implications of evaluating social intelligence using a test that evaluates general intelligence. For this purpose, we include other agents into an initially singleagent environment to figure out the issues that appear when evaluating an agent in the context of other agents. From this analysis we obtain useful information for the evaluation of social intelligence.From the lessons learned, we identify the components that should be considered in order to measure social intelligence, and we provide a formal and parametrised definition of social intelligence. This definition calculates an agent's social intelligence as its expected performance in a set of environments with a set of other agents arranged in teams and participating in lineups, with rewards being re-understood appropriately. This is conceived as a tool to define social intelligence testbeds where we can generate several degrees of competitive and cooperative behaviours. We test this definition by experimentally analysing the influence of teams and agent line-ups for several multi-agent systems with variants of Q-learning agents.However, not all testbeds are appropriate for the evaluation of social intelligence. To facilitate the analysis of a social intelligence testbed, we provide some formal property models about social intelligence in order to characterise the testbed and thus assess its suitability. Finally, we use the presented properties to characterise some social games and multi-agent environments, we make a comparison between them and discuss their strengths and weaknesses in order to evaluate social intelligence.ii ResumenBajo la visión de la inteligencia artificial, un agente inteligente es una entidad autónoma la cual interactúa en un entorno a través de observaciones y acciones, tratando de lograr uno o más ...

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“…One of the earliest results in the area is that generalised chess is EXPTIME-complete (Fraenkel & Lichtenstein, 1981). Amongst other games to have been proved NP-complete or harder are the card solitaire games Klondike (Longpré & McKenzie, 2009), Freecell (Helmert, 2003) and Black Hole (Gent, Jefferson, Kelsey, Lynce, Miguel, Nightingale, Smith, & Tarim, 2007), the Sudoku puzzle (Takayuki & Takahiro, 2003), video games like Pac-Man (Viglietta, 2014), and casual games such as Minesweeper (Kaye, 2000), Candy Crush Saga and Bejeweled (Walsh, 2014;Guala, Leucci, & Natale, 2014). Many other games are surveyed by Kendall, Parkes, and Spoerer (2008) and by Demaine and Hearn (2009).…”

Section: Introductionmentioning

confidence: 99%

Complexity of n-Queens Completion

Gent

Jefferson

Nightingale

2017

jair

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The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.

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Complexity results for standard benchmark domains in planning

Cited by 80 publications

References 6 publications

Refining complexity analyses in planning by exploiting the exponential time hypothesis

Refining complexity analyses in planning by exploiting the exponential time hypothesis

Towards a Universal Test of Social Intelligence

Complexity of n-Queens Completion

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