The Complexity of Robot Games on the Integer Line

Arul, Arjun; Reichert, Julien

doi:10.4204/eptcs.117.9

Cited by 9 publications

(16 citation statements)

References 5 publications

(9 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, we do not know yet whether EXPSPACE is an optimal upper bound, but we have the following lower bound. Theorem 6 ( [5,6]). Reach-CS 1 is EXPTIME-hard.…”

Section: Relative Integers Semanticsmentioning

confidence: 99%

See 1 more Smart Citation

On the Complexity of Counter Reachability Games

Reichert

2013

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

Counter reachability games are played by two players on a graph with labelled edges. Each move consists in picking an edge from the current location and adding its label to a counter vector. The objective is to reach a given counter value in a given location. We distinguish three semantics for counter reachability games, according to what happens when a counter value would become negative: the edge is either disabled, or enabled but the counter value becomes zero, or enabled. We consider the problem of deciding the winner in counter reachability games and show that, in most cases, it has the same complexity under all semantics. Surprisingly, under one semantics, the complexity in dimension one depends on whether the objective value is zero or any other integer.

show abstract

“…However, we do not know yet whether EXPSPACE is an optimal upper bound, but we have the following lower bound. Theorem 6 ( [5,6]). Reach-CS 1 is EXPTIME-hard.…”

Section: Relative Integers Semanticsmentioning

confidence: 99%

“…Reach-CS 1 is EXPTIME-hard. This lower bound is inherited from countdown games [5] and robot games [6], which we can express as counter reachability games.…”

Section: Relative Integers Semanticsmentioning

confidence: 99%

On the Complexity of Counter Reachability Games

Reichert

2013

Lecture Notes in Computer Science

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, studies on quantitative game theory and related algorithms for determining the optimal strategies [26,118,122,25,14,37,99], conducted for various formalisms, like, e.g., automata, are particularly relevant, as such games can be used as models to define the interaction between a system and its environment on the base of quantitative objectives and behaviours inducing costs, rewards, and resource consumption. The relation with model checking is strict, as also demonstrated by the most recent advances in tools like, e.g., PRISM and MCMAS, implementing model checking algorithms for MDPs founded on game semantics.…”

Section: Analysis Techniques and Tools: Program Analysis Model Checkmentioning

confidence: 99%

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

Aldini

2020

Electron. Proc. Theor. Comput. Sci.

View full text Add to dashboard Cite

Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the behaviour of many critical systems and in estimating their properties. Hence, they need to be integrated both at the level of system modeling and within the verification methodologies and tools. Along the last two decades a variety of theoretical achievements and automated techniques have contributed to make quantitative modeling and verification mainstream in the research community. In the same period, they represented the central theme of the series of workshops entitled Quantitative Aspects of Programming Languages and Systems (QAPL) and born in 2001. The aim of this survey is to revisit such achievements and results from the standpoint of QAPL and its community.

show abstract

“…Thus a winning strategy gives a way for a player to win, regardless of the way the opponent plays. Previously, it has been proved that deciding the winner in one-dimensional robot games, where integers are given in binary, is EXPTIME-complete [20].…”

Section: Introductionmentioning

confidence: 99%

“…Apart from the solution of the open problem, the main contribution of the first part is a collection of new, original encodings and constructions that allow simulating zero-checks and state space of a universal machine within a minimalistic two-dimensional system of two non-deterministic stateless players. Dimension 1 2 3 EXPTIME-complete [20] undecidable undecidable [21] Table 1: The results on complexity of deciding whether Eve has a winning strategy in robot games. Our result is in bold.…”

Section: Introductionmentioning

confidence: 99%

On decidability and complexity of low-dimensional robot games

Niskanen

Potapov

Reichert

2020

Journal of Computer and System Sciences

View full text Add to dashboard Cite

A robot game, also known as a Z-VAS game, is a two-player vector addition game played on the integer lattice Z n , where one of the players, Adam, aims to avoid the origin while the other player, Eve, aims to reach the origin. The problem is to decide whether or not Eve has a winning strategy. In this paper we prove undecidability of the two-dimensional robot game closing the gap between undecidable and decidable cases. We also prove that deciding the winner in a robot game with states in dimension one is EXPSPACE-complete and study a subclass of robot games where deciding the winner is in EXPTIME.

show abstract

The Complexity of Robot Games on the Integer Line

Cited by 9 publications

References 5 publications

On the Complexity of Counter Reachability Games

On the Complexity of Counter Reachability Games

Quantitative Aspects of Programming Languages and Systems over the past 2^4 years and beyond

On decidability and complexity of low-dimensional robot games

Contact Info

Product

Resources

About