Problem 221. Boolean algebra

Created by Tomasz

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Your contractor from Elbonia has sent you the prototype of the new logical unit. It turns out that the only logical relation it understands is "nand":<pre class="language-matlab">nand(a,b) := ~(a&b)
</pre>Your team has been developing code using the usual logical operators following MATLAB syntax: <tt>~,&</tt> and <tt>|</tt>. To save the project you need to write a translator that expresses MATLAB logical expressions using only the <tt>nand</tt> function.Input<ul><li>expr: a string containing a valid logical expression in MATLAB, that relates the two logical variables <tt>a</tt> and <tt>b</tt></li></ul>Output<ul><li>out: a string containing an equivalent logical expression that may only use the function <tt>nand(a,b)</tt>.</li></ul>Example 1:<pre> expr = 'a|(~b)'
 =>out = 'nand(nand(a,a),b)'</pre>Example 2:<pre> expr = '(a & ~a) | ~(a|b)'
 =>out = 'nand(nand(nand(a,a),nand(b,b)),nand(nand(a,a),nand(b,b)))'</pre>Remarks:It is not necessary to provide the shortest solution. A solution always exists. The input string is non-empty and always evaluates to true or false, if <tt>a</tt> and <tt>b</tt> are logical variables. All substrings in the output that are not 'a','b','0','1','true','false','(',')' or'nand' will be ignored.

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Solution 25396

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@bmtran (Bryant Tran) on 2 Feb 2012

Electrical Engineering Eduction FTW!

Tomasz on 2 Feb 2012

Nice! And since the eval-block, it's the only working solution for this problem so far.

@bmtran (Bryant Tran) on 6 Feb 2012

Apparently they blocked inline too now :(

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Problem 221. Boolean algebra

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