Difference between revisions of "Graphic equality"
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| + | $#C+1 = 9 : ~/encyclopedia/old_files/data/G045/G.0405020 Graphic equality | ||
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| + | A relation between two constructive objects (cf. [[Constructive object|Constructive object]]) which consists in the fact that the objects are constructed in the same way out of the same elementary tokens. Graphic equality of two words (cf. [[Word|Word]]) means that the words are composed of the same letters in the same sequence. Graphic equality of words may more precisely be formulated as follows: a) the empty word is graphically equal to itself only; b) two non-empty words $ P \xi $ | ||
| + | and $ Q \eta $( | ||
| + | where $ \xi $ | ||
| + | and $ \eta $ | ||
| + | denote the last letters of these words) are graphically equal if and only if $ P $ | ||
| + | and $ Q $ | ||
| + | are graphically equal and the letters $ \xi $ | ||
| + | and $ \eta $ | ||
| + | are identical. Graphic equality is usually denoted by the symbols | ||
| + | |||
| + | $$ | ||
| + | = _ \cdot ,\ {\underline \circ } bar . | ||
| + | $$ | ||
====References==== | ====References==== | ||
<table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: Trudy Mat. Inst. Steklov. 42 (1954))</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Markov, N.M. [N.M. Nagornyi] Nagorny, "The theory of algorithms" , Kluwer (1988) (Translated from Russian)</TD></TR></table> | <table><TR><TD valign="top">[1]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: Trudy Mat. Inst. Steklov. 42 (1954))</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Markov, N.M. [N.M. Nagornyi] Nagorny, "The theory of algorithms" , Kluwer (1988) (Translated from Russian)</TD></TR></table> | ||
Latest revision as of 19:42, 5 June 2020
A relation between two constructive objects (cf. Constructive object) which consists in the fact that the objects are constructed in the same way out of the same elementary tokens. Graphic equality of two words (cf. Word) means that the words are composed of the same letters in the same sequence. Graphic equality of words may more precisely be formulated as follows: a) the empty word is graphically equal to itself only; b) two non-empty words $ P \xi $
and $ Q \eta $(
where $ \xi $
and $ \eta $
denote the last letters of these words) are graphically equal if and only if $ P $
and $ Q $
are graphically equal and the letters $ \xi $
and $ \eta $
are identical. Graphic equality is usually denoted by the symbols
$$ = _ \cdot ,\ {\underline \circ } bar . $$
References
| [1] | A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russian) (Also: Trudy Mat. Inst. Steklov. 42 (1954)) |
| [2] | A.A. Markov, N.M. [N.M. Nagornyi] Nagorny, "The theory of algorithms" , Kluwer (1988) (Translated from Russian) |
How to Cite This Entry:
Graphic equality. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Graphic_equality&oldid=14050
Graphic equality. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Graphic_equality&oldid=14050
This article was adapted from an original article by N.M. Nagornyi (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article