discrete mathematics - BNF to EBNF conversion

I've trying to convert a given BNF list to EBNF and im completely clueless how. Can anyone help?The BNF is: <Sentence> :== <NounPhrase><VerbPhrase><NounPhrase> :== <Noun><NounPhrase> :== <Article><Noun><NounPhrase> :== <Article><AdjectiveList><Noun><NounPhrase> :== <AdjectiveList><Noun><AdjectiveList> :== <Adjective><AdjectiveList> :== <Adjective><AdjectiveList><VerbPhrase> :== <Verb><VerbPhrase> :== <Ver...Read more

discrete mathematics - Describing the right recurrence

I've to describe a recurrence for l_n, the number of lobsters caught in year nThe task says: A hobby fisherman estimates the number of lobsters he will catch in a year as the average of the number he caught in the two previous yearsDescribe a recurrence for l_n, the number of lobsters caught in year nI've tried something. It's degree-D homogeneous LRR so the recurrence is:l_n = l_n-1 + l_n-2 as it's for 2 years. Have I solved ít correctly?...Read more

discrete mathematics - Recurrence relation, how to handle fractional terms?

So I need to find a_30 for a recurrence relation defined by: a_n=2*a_n/2 + 1a_1=1Underscores dictate subscripts.The dilemma I run into: in order to find a_30, I must find a_15, but to find that I need a_7.5, which simply doesn't exist. How do I handle this? I also tried running it in Matlab, but it predictably terminated on a_3, citing the same type of nonexistent index....Read more

discrete mathematics - Find the recurrence relation

I'm new to recurrence relations and I'm having trouble figuring out this problem:Find a recurrence relation for the number of ways to make a stack of green, yellow, and orange napkins so that no two green napkins are next to each other.I've come up with a(n)=2a(n-1)+2a(n-2) but I'm not sure if that's right/ on the right track.Any help would be great!...Read more

Is there a tool that supports discrete mathematics?

Discrete mathematics (also finite mathematics) deals with topics such as logic, set theory, information theory, partially ordered sets, proofs, relations, and a number of other topics.For other branches of mathematics, there are tools that support programming. For statistics, there is R and S that have many useful statistics functions built in. For numerical analysis, Octave can be used as a language or integrated into C++. I don't know of any languages or packages that deal specifically with discrete mathematics (although just about every lang...Read more

Discrete mathematics problem - Probability theory and counting

I'm taking a discrete mathematics course, and I encountered a question and I need your help. I don't know if this is the right place for that though :)It says:Each user on a computer system has a password, which is six to eight characters long, where each character is an uppercase letter or a digit. Each password must contain at least one digit. How many possible passwords are there?The book solves this by adding the probabilities of having six,seven and eight characters long password. However, when he solves for probability of six characters h...Read more

Predicates and quantifiers. (Discrete mathematics)

I would like to be sure that my answer is true.the question is :Let I (x) be the statement “x has an Internet connection”and C(x, y) be the statement “x and y have chatted overthe Internet,” where the domain for the variables x and yconsists of all students in your class. Use quantifiers toexpress each of these statements:** Exactly one student in your class has an Internet connection.my answer is: ∃x∀y(x=y ↔ I(y))....Read more