Image Analysis and Computer Vision

Theoretical Computer Science: Exploring New Frontiers of Theoretical Informatics

Let /? be a real number > 1. Addition and multiplication by a fixed positive integer of real numbers represented in bsise /3 cire shown to be computable by an on-line algorithm, and thus are continuous functions. When /? is a Pisot number, these functions cire computable by an on-line finite automaton.

Mathematical Foundations of Computer Science 1999

Image analysis and computer vision: 1999

Image Analysis and Computer Vision: 1998☆

Recently, related to the open problem of whether deterministic and nondeterministic space (especially lower-level) complexity classes are separated, the inkdot Turing machine was introduced. An inkdot machine is a conventional Turing machine capable of dropping an inkdot on a given input tape for a landmark, but not to pick it up nor further erase it. In this paper, we introduce a finite state version of the inkdot machine as a weak recognizer of the properties of digital pictures, rather than a Turing machine supplied with a one-dimensional working tape. We first investigate the sufficient spaces of three-way Turing machines to simulate two-dimensional inkdot finite automaton, as preliminary results. Next, we investigate the basic properties of two-dimensional inkdot automaton, i.e. the hierarchy based on the number of inkdots and the relationship of two-dimensional inkdot automata to other conventional two-dimensional automata. Finally, we investigate the recognizability of connected pictures of two-dimensional inkdot finite machines.

The effect of inkdots for two-dimensional automata

A note on two-dimensional probabilistic finite automata

This paper investigates the space hierarchies of the language classes for two-dimensional Turing machines (2-TM's), two-dimensional pushdown automata (2-PDA's) and two-dimensional counter automata (2-CA's) with small space. We show that (1) if L(n) is space constructible by a 2-TM, L(n) ≤ log n and L′(n) = o(L(n)), then strong 2-DSPACE(L(n)) – weak 2-ASPACE(L′(n)) ≠ ∅, (2) if L(n) is space constructible by a 2-PDA, L(n) ≤ log n and L′(n) = o(L(n)), then strong 2-DPDA(L(n)) – weak 2-ASPACE(L′(n)) ≠ ∅, and (3) if L(n) is space-constructible by a 2-CA, L(n) ≤ n and L′(n) = o(L(n)), then strong 2-DCA(L(n)) – weak 2-ACA(L′(n)) ≠ ∅, (4) where strong 2-DSPACE(L(n)) (strong 2-DPDA(L(n)), strong 2-DCA(L(n))) denotes the class of sets accepted by strongly L(n) space-bounded deterministic 2-TM's (2-PDA's, 2-CA's), and weak 2-ASPACE(L′(n)) (weak 2-ACA(L′(n))) denotes the class of sets accepted by weakly L′(n) space-bounded alternating 2-TM's (2-CA's). We also investigate the closure property of space-bounded alternating 2-PDA's and 2-CA's under complementation, and show that (1) if L(n) = o(log log n), then the class of sets accepted by L(n) space-bounded alternating 2-PDA's is not closed under complementation, and (2) if L(n) is space-constructible by a 2-CA, L(n) ≤ n and , then the class of sets accepted by L′(n) space-bounded alternating 2-CA's is not closed under complementation.

Space hierarchies of two-dimensional alternating turing machines, pushdown automata and counter automata

This paper introduces two-dimensional probabilistic Turing machines (2-ptm's), and investigates several properties of them. We first investigate a relationship between two-dimensional alternating finite automata (2-afa's) and 2-ptm's with error probability less than 12 and with sublogarithmic space, and show that there is a set of square tapes accepted by 2-afa, but not recognized by any o(log-n) space-bounded 2-ptm with error probability less than 12. This partially solves an open problem in Okazaki et al. (Inform. Sci., to appear). We next investigate a space hierarchy of 2-ptm's with error probability less than 12 and with sublogarithmic space, and show that if L(n) is space-constructible by a two-dimensional Turing machine, there is a set of square tapes accepted by a strongly L(n) space-bounded two-dimensional deterministic Turing machine, but not recognized by any L(n) space-bounded 2-ptm with error probability less than 12.

https://repository.kulib.kyoto-u.ac.jp/dspace/bitstream/2433/62062/1/1041-19.pdf

Yue Wang

Papers

The effect of inkdots for two-dimensional automata

A note on two-dimensional probabilistic finite automata

Space hierarchies of two-dimensional alternating turing machines, pushdown automata and counter automata

A Note on Two-dimensional Probabilistic Turing Machines (Algorithms and Theory of Computing)

Alternating Rebound Turing Machines (Special Section on Discrete Mathematics and Its Applications)