# Questions tagged [rewriting-systems]

For questions related to (term) rewriting systems (which are reduction systems in which rewrite rules apply to terms).

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### Mitchell Foundations for PL 2.3.4 (observational equivalence)

Background. The language is PCF, with observable types $\text{bool}$ and $\text{nat}$. $\text{eval}$ is the partial function on PCF terms such that $\text{eval}(M) = N$ iff $N$ is the unique normal ...
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### How does confluence apply (or not) in non-terminating rewriting systems?

Suppose we have the rules $\{x\to Ax, x \to xB\}$. We start with letting $x$ be the empty string, and are free to apply either rule at will. This will allow us to build any string of form $A^mB^n$. ...
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I am currently learning how to factorise quadratic expressions of the form $ax^2 + bx + c$. In my textbook (Foundations math seventh edition) they are elaborating on a particular way of finding a ...
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### Fewest applications of associativity

By repeatedly applying the basic associativity law $(x+y)+z = x+(y+z)$, one can get from any one expression with binary addition to any other with the variables in the same order. Specifically, given ...
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### a locally confluent and terminatting rewrite system is complete

I want to prove that every locally confluent rewrite system is confluent. Since I know very little about rewrite systems and logic, I tried looking at it as a digraph with no external infinite paths ...
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### What is this constant 'C' in integration? Why is it different when I integrate using different techniques?

Method 1: Method 2: In these two images, you will see that I have integrated $\sin^3 x$ using different techniques. As you can see I get different answers. I asked my teacher why this is and he said ...
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### A question about a confluent abstract rewriting system?

Let $(A,\rightarrow)$ be a confluent abstract rewriting system. Assume that $a\stackrel{*}\rightarrow b$, $a\stackrel{*}\rightarrow c$ is a fork. Then $b,c$ is joinable, that is, there is a $d\in A$ ...
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### How to extract PID parameters from a controller in zpk form?

I have a plant of 3th order, e.g.: $$G(s)=\frac{5}{(s+2)(s^2+2s+4)}$$ that I want to control by tracking the reference. Now I need to have a fast response, zero steady-state error and low overshoot. ...
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### A question about how to check a rewriting system is confluent?

I am reading the book "Computation with finitely presented groups" on page 59, I don't know why we need only test six words? does any other words can be generated by the six words? it is seems not.
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### Special Sequences, homework

I'm preparing for my mathematics exam and I am stuck on something which I believe should be simple. The question is as follows: A rough estimate of the total oil and gas reserves of a country at the ...
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### Prove confluence

I have these 2 questions to prove or disprove confluence. 1) Answer 2) Answer Now I am having difficulty understanding these. Aren't these 2 questions same? then why in one case it is confluent ...
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An Abstract rewriting system is a set A, whose elements are usually called objects, together with a binary relation on A, traditionally denoted by $\rightarrow$. An object $x \in A$ is called ...