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our dfas are required to have exactly one edge incident from each state for each input symbol so there is a unique next state for every current state
the equivalence problem is the question of whether two languages are equal in the sense of being the same set of strings an instance is a pair of
the universality problem is the dual of the emptiness problem is la sigmalowastit can be solved by minor variations of any one of the algorithms for
the fact that the recognition problem is decidable gives us another algorithm for deciding emptiness the pumping lemma tells us that if every string
the myhill-nerode theorem provided us with an algorithm for minimizing dfas moreover the dfa the algorithm produces is unique up to isomorphism every
the emptiness problem is the problem of deciding if a given regular language is empty emptytheorem 4 emptiness the emptiness problem for regular
the recognition problem for a class of languages is the question of whether a given string is a member of a given language an instance consists of a
for example the question of whether a given regular language is positive does not include the empty string is algorithmically decidablepositiveness
well close our consideration of regular languages by looking at whether certain problems about regular languages are algorithmically
applying the pumping lemma is not fundamentally dierent than applying general sux substitution closure or the non-counting property the pumping lemma
for every regular language there is a constant n depending only on l such that for all strings x isin l if x ge n then there are strings u v and w
the fact that regular languages are closed under boolean operations simplies the process of establishing regularity of languages in essence we can
this was one of the rst substantial theorems of formal language theory its maybe not too surprising to us as we have already seen a similar
all that distinguishes the denition of the class of regular languages from that of the class of star-free languages is that the former is closed
lto was the closure of lt under concatenation and boolean operations which turned out to be identical to sf the closure of the nite languages under
computer has a single fifo queue of xed precision unsigned integers with the length of the queue unbounded you can use access methods similar to
computer has a single lifo stack containing xed precision unsigned integers so each integer is subject to overow problems but which has unbounded
computer has a single unbounded precision counter which you can only increment decrement and test for zero you may assume that it is initially zero
first model computer has a xed number of bits of storage you will model this by limiting your program to a single xed-precision unsigned integer
the objective of the remainder of this assignment is to get you thinking about the problem of recognizing strings given various restrictions to your
when we study computability we are studying problems in an abstract sense for example addition is the problem of having been given two numbers
prepare the consolidated financial statements for the year ended 30 june 2011on 1 july 2006 mark ltd acquired all the share capitall of john ltd for
a common approach in solving problems is to transform them to different problems solve the new ones and derive the solutions for the original
a problem is said to be unsolvable if no algorithm can solve it the problem is said to be undecidable if it is a decision problem and no algorithm
different types of applications and numerous programming languages have been developed to make easy the task of writing programs the assortment of