The IEEEtran's documentation suggests:
B. Algorithms
IEEE publications use the figure environment to contain
algorithms that are not to be a part of the main text flow. Peter
Williams’ and Rogerio Brito’s algorithmic.sty package [24] or Szász
János’ algorithmicx.sty package [25] (the latter is designed to be
more customizable than the former) may be of help in producing
algorithm-like structures (although authors are of course free to use
whatever LaTeX commands they are most comfortable with in this
regard). However, do not use the floating algorithm environment of
algorithm.sty (also by Williams and Brito) or algorithm2e.sty (by
Christophe Fiorio) as the only floating structures IEEE uses are
figures and tables. Furthermore, IEEEtran will not be in control of
the (non-IEEE) caption style produced by the algorithm.sty or
algorithm2e.sty float environments.
So, as suggested, do not use the algorithm floating environment; you can wrap your algorithm inside a figure (or figure*) environment (if a caption is required and the captions are to be IEEEtran compliant) and use the algorithmicx package ; something like this:
\documentclass{IEEEtran}
\usepackage{algpseudocode}
\begin{document}
\begin{figure}
\begin{algorithmic}[1]
\Procedure{Euclid}{$a,b$}\Comment{The g.c.d. of a and b}
\State $r\gets a\bmod b$
\While{$r\not=0$}\Comment{We have the answer if r is 0}
\State $a\gets b$
\State $b\gets r$
\State $r\gets a\bmod b$
\EndWhile\label{euclidendwhile}
\State \textbf{return} $b$\Comment{The gcd is b}
\EndProcedure
\end{algorithmic}
\caption{Euclid's algorithm}\label{euclid}
\end{figure}
\end{document}
If no caption is required, then simply don't use the figure environment.
Is this what you are trying to achieve?
This is the MWE:
\documentclass{article}
\usepackage[plain]{algorithm}
\usepackage{algpascal}
\begin{document}
\algrenewcommand\textkeyword{\textrm}
\algdef{SE}{For}{End}[2]{%
\textkeyword{for} \(#1\) \textkeyword{to} \(#2\) \textkeyword{do begin}}{%
\textkeyword{end}}
\begin{algorithm}
\begin{algorithmic}[1]
\State Assign an ordering $A_{1}, ..., A_{n}$ to the nonterminals of the grammar.
\For{i = 1}{n}
\For{j = 1}{i-1}
\State for each production of the form $A_{i} \rightarrow A_{j} \alpha$
\End
\End
\end{algorithmic}
\caption{Paull's algorithm}
\end{algorithm}
\end{document}
Explanation
To match your first two requests, I've redefined the behavior of for to have an end statement by adding the lines:
\algdef{SE}{For}{End}[2]{%
\textkeyword{for} \(#1\) \textkeyword{to} \(#2\) \textkeyword{do begin}}{%
\textkeyword{end}}
To match your last request, it suffices to add the line:
\algrenewcommand\textkeyword{\textrm}
which redefines the font for keywords to be \textrm instead of \textbf.
In regards of your 3rd request, there are two ways.
If you want the algorithm to behave as an algorithm, simply load the algorithm package with the option plain as in the above MWE:
\usepackage[plain]{algorithm}
If you want the algorithm to behave as a figure, there is no need to load the algorithm package, simply insert the algorithmic environment inside a figure, i.e. replace the lines
\begin{algorithm}
\begin{algorithmic}[1]
...
\end{algorithmic}
\caption{Paull's algorithm}
\end{algorithm}
with
\begin{figure}
\begin{algorithmic}[1]
...
\end{algorithmic}
\caption{Paull's algorithm}
\end{figure}
and you will have
Addendum
This is the complete implementation of the algorithm in the figure:
\documentclass{article}
\usepackage[plain]{algorithm}
\usepackage{algpascal}
\begin{document}
\algrenewcommand\textkeyword{\textrm}
\algdef{SE}{For}{End}[2]{%
\textkeyword{for} \(#1\) \textkeyword{to} \(#2\) \textkeyword{do begin}}{%
\textkeyword{end}}
\algdef{SE}{ForEach}{End}[1]{%
\textkeyword{for each} #1 \textkeyword{do begin}}{%
\textkeyword{end}}
\begin{algorithm}
\begin{algorithmic}[1]
\State Assign an ordering $A_{1}, \dots, A_{n}$ to the nonterminals of the grammar.
\For{i := 1}{n}
\For{j := 1}{i-1}
\ForEach{production of the form $A_{i} \rightarrow A_{j} \alpha$}
\State remove $A_{i} \rightarrow A_{j} \alpha$ from the grammar
\ForEach{production of the form $A_{j} \rightarrow \beta$}
\State add $A_{i} \rightarrow \beta\alpha$ to the grammar
\End
\End
\End
\State transform the $A_{i}$-productions to eliminate direct left recursion
\End
\end{algorithmic}
\caption{Paull's algorithm}
\end{algorithm}
\end{document}
There is the need to define a new command \ForEach:
\algdef{SE}{ForEach}{End}[1]{%
\textkeyword{for each} #1 \textkeyword{do begin}}{%
\textkeyword{end}}
Note that I've defined \ForEach so to take one "text" argument, because it seemed to me the best way to define it.
If you want it to take a "math" argument, then define it as
\algdef{SE}{ForEach}{End}[1]{%
\textkeyword{for each} \(#1\) \textkeyword{do begin}}{%
\textkeyword{end}}
and use it as follows (amsmath is needed for the command \text):
\ForEach{\text{production of the form }A_{i} \rightarrow A_{j} \alpha}
Best Answer
\Statedoes not receive an argument; just useHowever, your typesetting is inconsistent. Use math when needed.