Automata on a 2-dimensional tape

Blum, Manuel; Hewitt, Carl

doi:10.1109/focs.1967.6

Cited by 183 publications

(98 citation statements)

References 4 publications

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“…However, this limitation is inherent and not confined to our formalisation since the parameterised verification problem even for one robot (k = 1) on a grid with only "local" tests is undecidable [6,30]. A second limitation is that robots do not have a rich memory (e.g., they cannot remember a map of where they have visited).…”

Section: Discussionmentioning

confidence: 99%

“…In [6,30] (see also the discussion before Theorem 1) it was shown that the PVP is undecidable for two synchronous robots on a line, reachability tasks, and allowing the robots "remote" position-tests. In Section 4.1 we substantially strengthen this result and prove that the problem is still undecidable even if we only allow robots "local" position-tests or even just local "collision tests", both for robots that move synchronously and asynchronously.…”

Section: Discussionmentioning

confidence: 99%

“…6 Add to every transition of robot R i , for i ∈ {0, 1, 2, 3}, the additional guard that M is on the same node with it. Thus, M enables the synchronisation robots to move, and if M ever stops, then so does the simulation.…”

Section: Undecidability Of Multi-robot Systems On a Linementioning

confidence: 99%

See 2 more Smart Citations

Verification of Asynchronous Mobile-Robots in Partially-Known Environments

Aminof

Murano

Rubin

et al. 2015

PRIMA 2015: Principles and Practice of Multi-Agent Systems

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Abstract. This paper establishes a framework based on logic and automata theory in which to model and automatically verify that multiple mobile robots, with sensing abilities, moving asynchronously, correctly perform their tasks. The motivation is from practical scenarios in which the environment is not completely know to the robots, e.g., physical robots exploring a maze, or software agents exploring a hostile network. The framework shows how to express tasks in a logical language, and exhibits an algorithm solving the parameterised verification problem, where the graphs are treated as the parameter. The main assumption that yields decidability is that the robots take a bounded number of turns. We prove that dropping this assumption results in undecidability, even for robots with very limited ("local") sensing abilities.

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Verification of Asynchronous Mobile-Robots in Partially-Known Environments

Aminof

Murano

Rubin

et al. 2015

PRIMA 2015: Principles and Practice of Multi-Agent Systems

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“…Here we remind only four of them and we refer to [36] for a survey on different models of finite automata recognizing picture languages. The first model, called 4-way finite automaton, shortly 4FA, was proposed in 1967 by Blum and Hewitt [10]. It is an extension of 2-way finite automata for strings and allows the finite automaton to move in four directions: t, b, l, r (top, bottom, left, and right).…”

Section: Models Of 2-dimensional Finite Automatamentioning

confidence: 99%

Picture Languages: From Wang Tiles to 2D Grammars

Cherubini

Pradella

2009

Algebraic Informatics

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“…Therefore, the problem of computational complexity was also arisen in the two-dimensional information processing. Blum and Hewitt first proposed two-dimensional automata -two-dimensional finite automata and marker automata, and investigated their pattern recognition abilities in 1967 [1]. Since then, many researchers in this field have been investigating a lot of properties about automata on a two-dimensional tape [11].…”

Section: Introductionmentioning

confidence: 99%