I am using the Java API of Z3 and I need to define integer variables which are natural i.e. their value cannot be negative. How can I define natural data type in z3 using java API?
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It depends on the version of Java. Pre-Java 8 you have to roll your own type, often by using larger primitives so you can represent the entire range of an unsigned value at the bit-length you require.
This (may) require doing your own two's complement math.
Java 8 has a new Unsigned Integer API, which offer a much easier way of manipulating values in a truly unsigned manner. See the API docs for Integer.