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construct a mealy machine that can output even or odd according to the total no of 13939s encountered is even or
spam messages h 98 m 90 l 80 non spam h12 m 8 l 5 the organization estimates that 75 of all messages it receives are spam messages if the
construct a pda that accepts xy x y in a b such that x y and xi yi for some i 1 i minx y for your pda to work correctly it will need
a turing machine is a theoretical computing machine made-up by alan turing 1937 to serve as an idealized model for mathematical calculation a turing
design a turing machine to compute x y xy gt 0 with x an y in unary seperated by a descrition and genereal idea is needed no need for all tm
the project 2 involves completing and modifying the c program that evaluates statements of an expression language contained in the expression
theorem myhill-nerode a language l sube sigma is recognizable iff equivl partitions sigma into nitely many nerode equivalence classesproof for the
this close relationship between the sl2 languages and the recognizable languages lets us use some of what we know about sl2 to discover properties of
theorem the class of nite languages is a proper subclass of sl note that the class of nite languages is closed under union and concatenation but sl
we have now dened classes of k-local languages for all k ge 2 together these classes form the strictly local languages in generaldenition strictly
the k-local myhill graphs provide an easy means to generalize the suffix substitution closure property for the strictly k-local languageslemma
the generalization of the interpretation of strictly local automata as generators is similar in some respects to the generalization of myhill graphs
myhill graphs also generalize to the slk case the k-factors however cannot simply denote edges rather the string sigma1sigma2 sigmak-1sigmak asserts
strictly 2-local automata are based on lookup tables that are sets of 2-factors the pairs of adjacent symbols which are permitted to occur in a word
while the sl2 languages include some surprisingly complex languages the strictly 2-local automata are nevertheless quite limited in a strong sense
exercise give a construction that converts a strictly 2-local automaton for a language l into one that recognizes the language lr justify the
exercise show using suffix substitution closure that l3 l3 isin sl2 explain how it can be the case that l3 l3 isin sl2 while l3 l3 sube l3 and l3
let l3 aibcj i j ge 0 give a strictly 2-local automaton that recognizes l3 use the construction of the proof to extend the automaton to one that
one might assume that non-closure under concatenation would imply non closure under both kleene- and positive closure since the concatenation of a
intuitively closure of sl2 under intersection is reasonably easy to see particularly if one considers the myhill graphs of the automata any path
the key thing about the suffx substitution closure property is that it does not make any explicit reference to the automaton that recognizes the
our primary concern is to obtain a clear characterization of which languages are recognizable by strictly local automata and which arent the view of
another way of interpreting a strictly local automaton is as a generator a mechanism for building strings which is restricted to building all and
to see this note that if there are any cycles in the myhill graph of a then la will be infinite since any such cycle can be repeated
in exercise 9 you showed that the recognition problem and universal recognition problem for sl2 are decidable we can use the structure of myhill