For each of the following three languages over Σ = {a,b}, provide a regular expression and a DFA for the language. your automata should have at most 10 states. 1. The set of strings that contain abbab, in that order, but not necessarily con- secutively. Said differently, the set of strings such that one can delete some amount of letters, possibly zero, to obtain abbab. For example, aaababaababba is in the language, while bbbababbbaa is not. 2. The set of strings of length 4 that contain exactly two bs. For example, abba is in the language, while abbb and abb are not. 3. The set of strings that contain exactly three as and an even number of bs. For example, abababb is in the language, while ababab is not.

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Problems on Turing Machines

In the computational world, the Turing machine is a powerful computation engine. The invention of the Turing Machine is done by Alan Turing in 1936. A Turing Machine (TM) is a diagrammatic model of a fictional computer. It determines an output from a set of input variables using a pre-defined set of rules. It is used to get around the limitations of finite automata and pushdown automata.