Reasoning About Strings This homework explores a logic over strings of the symbols 0 and 1. We define strings as either the empty string e, or as a (finite, but potentially arbitrarily long) series of Os and 1s. For example, the following are strings 0 0010 11111 10100100010000 We can also concatenate strings. If w and v are strings, we write their concatenation as wv. For example: 010^101 = 010101 010 = 010 01 0101 = 010101 101 = 101 To reason about strings, we have two atomic predicates. The first is string equality, written w = v. For example, the following predicates hold: 1010 = 1010 10 10 = 1010 Vw.w = w In contrast, the following predicates do not hold: 1010 = 0101 0101 = 101Vw.w = ww Our second atomic predicate is the substring predicate, written w [ v. The predicate w S v holds if w appears in order in v. For example, the following predicates hold: 01