Transformational Proof Notes
As the number of distinct primes (variables) increases,
the number of rows in a truth table increases exponentially.
In the worst case, shorter truth-table method requires looking at as many cases as
rows in the truth table
Mathematical Model Notes
In some areas (e.g., computing) the only means of modeling is abstract and
mathematical.
A computation is a process of deriving the possible values of a set of unknowns
using a mathematical model.
Can be performed by a human wi
Transformation Notes Procedure to transform any wff into a logically equivalent wff in CNF Step 1. Eliminate 's (Law of Equivalence) Step 2. Eliminate 's (Law of Implication) Step 3. Move 's inwards (De Morgan's Laws), eliminating any double negations (La
Command Language Notes
Dijkstras GCL (Guarded Command Language) is a generalization of
conventional imperative programming languages.
Its part of a notation widely used in formal reasoning about programs.
First rigorously develop a program in GCL.
The
Logic Notes
Logic makes a discipline scientific:
Deduce statements making up the discipline from a small number of
explicitly stated facts and hypotheses.
First logic as a language that allows us to express things precisely.
Then consider ways to reas
Validity Notes
Introduce terminology used in place of tautology and contradiction when we
come to predicate logic
Define syntactic forms for propositional logic wffs s.t.
any wff can be transformed into any one of these forms in a finite number
of tran
Lecture 1 Notes
Introduce terminology used in place of tautology and contradiction when we
come to predicate logic
Define syntactic forms for propositional logic wffs s.t.
any wff can be transformed into any one of these forms in a finite number
of tra
Lecture 2 Notes
Dijkstras GCL (Guarded Command Language) is a generalization of
conventional imperative programming languages.
Its part of a notation widely used in formal reasoning about programs.
First rigorously develop a program in GCL.
Then trans
Lecture 3 Notes
In some areas (e.g., computing) the only means of modeling is abstract and
mathematical.
A computation is a process of deriving the possible values of a set of unknowns
using a mathematical model.
Can be performed by a human with pencil
Lecture 4 Notes
Logic makes a discipline scientific:
Deduce statements making up the discipline from a small number of
explicitly stated facts and hypotheses.
First logic as a language that allows us to express things precisely.
Then consider ways to
Logic Laws Notes
Procedure to transform any wff into a logically equivalent wff in CNF
Step 1. Eliminate s (Law of Equivalence)
Step 2. Eliminate s (Law of Implication)
Step 3. Move s inwards (De Morgans Laws), eliminating any double negations (Law
of Ne
Predicate Logic Notes
Predicate logic extends the syllogistic notion of predicate to include relations.
And it incorporates all of propositional logic
thus the ability to reason about arbitrarily complex sentences.
Besides proposition symbols, we need
Proposition Notes
A proposition is a declarative sentence (true or false).
A proposition has a truth value: either T or F.
A proposition without a connective is an atomic or prime proposition.
Compound propositions are built up from prime propositions
Semantic Notes
What meanings (truth values) are given to prime propositions isnt addressed by
logic.
Need recursive rules so that,
given the truth values of the constituent primes,
we can determine the truth value of a proposition of any complexity.
Tautology Notes
2 ways to show 2 formulae logically equivalent:
using truth tables and
transformational proofs.
If 2 formulae are logically equivalent,
an occurrence of one in a formula can be replaced by an occurrence of the other
Replace equals wit
Linear Time Construction of
Suffix Tree
Presented By
Dr. Shazzad Hosain
Asst. Prof. EECS, NSU
High-level of Ukkonens Algorithm
Ukkonens algorithm is divided into m phases. In phase i+1,
tree i+1 is constructed from i
Each phase i+1 is further divided in