Show that if a DFA with exactly 5 states accepts a string of length 6, the language it accepts must be infinite.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
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Show that if a DFA with exactly 5 states accepts a string of length 6, the language it accepts must be
infinite. 

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Given that, the DFA with exactly 5 states accepts a string of length 6, the language it accepts must be infinite.

If we take 5 states, then four length input string is formed without any loops. Because, between two states one input is present. So, with 5 states length 4 string is formed. So, if we want to accept that DFA of string length then it must contains intermediate loops.

If it contains loops, then any length of the strings can be accepted by the DFA which is infinite by iterating the loops many times.

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