self made doubt

Question

How to know that the language needs 1 stack or more than one stack in order to know about it is regular, context-free or not.
example
L1={$a^i b^j c^k│i<j<k$}
L2={$a^i b^j c^k│i<j \  or \ k<j$}
L3={$a^i b^j c^k│i<j \ and \ k<j$}

Answer 1

$\boldsymbol{{\color{Blue}{ L1-CSL}}}$,      as we can see I,j, k are involving with two comparison at the time ,we can't do this with one stack ,two stack is required because at a time we should have to remember two aplhabet ,so it can be done  by CSL not by Cfl.

${\boldsymbol{\color{Blue}{L2-CFL}} }$,    yes we can see j is involving with( i or k )one comparison at time ,so we can do this by one stack .either j is comparing with i or comparing with k one at a time ,no need of two stack .

${\boldsymbol{\color{Blue}{L3-CSL}} }$,  this is almost same as first one but here j is greater than both ,here also j is involving with i and k with two comparison at a time{ j >I and j>k},so two stack required.so  csl.

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So remember one thing when one symbol is involving with two or more two comparison at a time then it can't be cfl.

Comments

thanks, @prateek I will apply this technique in other questions