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CSC701 Automata Theory And Formal Language UITM Assignment Example Malaysia

This course will examine the fascinating world of finite automata. Finite automata are used to model hardware and software, including components in compilers for computer languages such as Java or C# that need programming logic gates with input/output capabilities – but they’re way more than just a language construct! The study of abstract grammar has close links into this topic; it’s incorporated because formal “grammar” has many similarities when we think about abstract machines such as those made out from simple models like Turing Machine which can be considered one step closer towards understanding what an actual computer looks like.

The course will also cover the fascinating world of language theory, where we can extend finite automata so that they are capable of recognizing (and generating) sets or languages with an infinite number of words. Finally, the course will introduce practical programming problems in parsing languages for compilers and related tasks which can be solved using solutions available in modern compilers.

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The beauty of automata theory is that it provides a solid theoretical underpinning for our understanding of how computers work, and at the same time enables us to solve interesting practical programming problems. We will see this in action as we progress through the course.

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Assignment Brief 1: Explain how the relevant theories pertaining to respective models of computation

Computational models are theoretical frameworks of how computing devices get their tasks done. Broadly, there are two primary types of computational models, which are sequential computation and parallel processing.

A sequential computation is one in which a computer executes instructions in the order they were given. This type of mechanical process would fit well with a machine that relies on logic gates to calculate results in predetermined ways. Single-core CPUs execute instructions in the order they were set out by software without any parallelization – these CPUs can only handle one instruction at a time. It’s for this reason that when performing resource-intensive activities like running simulations or rendering graphics, multiple cores or even many cores will often need to chug along concurrently to complete the job quickly enough.

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Parallel processing is a computer design that consists of multiple functional units which simultaneously carry out operations. This type of computation is more closely related to the human brain, which has billions and billions of neurons firing off in different regions and at different frequencies to enable our brains to function. Parallel computing allows for these types of complex jobs to be completed much faster than with sequential computation.

There are different types of parallel processors, but the most common and well-known is the SIMD (single instruction, multiple data). SIMD processors can handle more than one data item at a time, which is why they’re often used for graphics rendering and physics simulations. They contain a number of simple processing cores which can handle simple math or logical operations. These processors are great for running simulations because they allow the same algorithms to be applied in parallel to each data item.

Assignment Brief 2: Construct a relevant automata based on a given grammar and vice versa

Automata cannot be constructed from grammar, since automata are the output of the process of constructing a given grammar. However, if one is given an automaton, they can construct a grammar to generate that language by looking at the states traversed by the finite-state machine and noting each state’s take precedence in relation to other non-final states both leaving or entering it . This would be done in order to determine if certain rules increase or decrease in probability as consecutive language elements become closer together irrespective of cross-reference with other rules.

The converse also holds true: every deterministic context-free parsing algorithm constructs a corresponding underlying automaton. In this manner, one could generate grammar from languages bound by algorithms.

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The derivation of grammar from an automaton is also known as the conversion of an automaton to grammar. The process begins with the definition of the following symbols, which will be used in the grammar:

  • Start symbol: This is the symbol that represents the beginning of the input string. In most cases, this will be the only symbol in the language that does not have a derivation starting from it.
  • Non-terminal symbols: These are symbols that represent the different parts of the input string and will be used to build up more complex words or phrases. In formal context-free grammars, these symbols are usually enclosed in angle brackets < >, while in regular expressions they are written as a word followed by a colon.
  • Terminal symbols: These are the symbols that represent the individual characters in the input string. In formal context-free grammars, these symbols are usually written as lowercase letters, while in regular expressions they are written as normal characters.

The starting symbol is then introduced into the grammar. The parser continues to insert rules until it can no longer recognize any more words because of syntactic ambiguity, in which case the set of possible derivations is complete.

Assignment Brief 3: Build a program for the automata based on the formal languages given

The automata are built based on the rules of recognition or generation that are given. If no generation or recognition rules are defined, then the automaton is said to be undefined meaning that it lacks an input state for which output can be produced. There are many different types of input/output symbols, so having a formal list of symbols should not be considered an essential requirement for building any type if suitable ones can be invented while building the automaton.

As an example, the following automaton recognizes the language consisting of all strings over the alphabet {a, b} that contain at least one a:

The states in this automaton are S0, S1, and S2. The input string “aba” is recognized by the automaton because it starts in state S0, goes to state S1 upon encountering the first a, and then goes to state S2 after encountering the second a.

The following automaton, which is defined using the regular expression “a*b”, generates all strings over the alphabet {a, b} that contain at least one a:

The following automaton, which is defined using the regular expression “a+(b+)*”, recognizes all strings over the alphabet {a, b} that contain at least one copy of a:

The states in this automaton are S0, S1, and S2. The input string “aba” is recognized by the automaton because it goes from state S0 to state S2 upon encountering a b.

In general, an automaton may have any finite number of states, and the transition function (or transition relation) determines which symbol (or state) the automaton will move to upon encountering a particular symbol (or state) in the input string. In addition, the start state and end state are always defined for an automaton. The start state is the state that the automaton will move to when it first starts processing the input string, and the end state is the final state that the automaton will move to when it terminates processing the input string.

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