A Brutal Look at Balanced Parentheses, Computing Machines, and Pushdown Automata

[macintux]

One of the few lessons I distinctly remember from college was finite automata in my PL class. I really enjoyed exploring the concepts and writing a grep tool; we were supposed to write either a NFA or DFA processing application, but I decided to write both.

20 years later I got to apply some of the same ideas to a language processing application, and it was such a pleasure to actually use something conceptual like that. Made me briefly regret landing in more hybrid infrastructure/automation roles instead of pure software development.

Somewhere I may still have my copy of Preperata and Yeh that my professor recommended at the time for further reading. Like most of my books, it was never actually read, just sat around for years.

[userbinator]

we’ll ask, “What’s the simplest possible computing machine that can recognize balanced parentheses?”

A counter. That's the difference between theory and practice. Because in practice, everything is finite.

[jibal]

The counter is simply the stack depth without bothering with the actual stack. If the stack is empty when you encounter a closer then it's unbalanced. If the stack isn't empty when you reach the end of the input then the items in the stack are unbalanced.

If you have multiple kinds of brackets then you need the same number of counters. Each counter corresponds to the number of openers of that type currently on the stack. EDIT: this is wrong. Counters can't distinguish between [() and ([)

If you're writing a parser and you want to report the location of an unclosed opening bracket then you need the actual stack.

[nmadden]

> Because in practice, everything is finite.

Indeed! https://neilmadden.blog/2019/02/24/why-you-really-can-parse-...

[testaccount28]

you don't need a full counter. increment, decrement, and check_if_zero are enough. no need for get_value.

[pfortuny]

Yes. Actually, a more interesting example which does not complicate the statement (not the problem) too much is to check for nested parenthesis and brackets:

(([[()])) -> ok ((([](])) -> not ok

Hope OP gets this message.

[praptak]

"But on a day-to-day basis, if asked to recognize balanced parentheses?"

On day-to-day basis you will never encounter this problem in pure form. As the consequence the solutions are not good for the day-to-day stuff.

Even if you only are only writting a verifier (which is already a bit unrealistic), you'll need to say something more than "not balanced". Probably rather something along the lines of "closing brace without a matching opening at [position]" or "[n] unclosed parentheses at <end of stream>" which rules out the simple recursive regex approach (counter still works).

[jibal]

To report the location of an unclosed opener you need a stack.

[senorqa]

The pictures of Brutalist architecture are awesome!

[sevensor]

I was hoping for more captions on those, they’re quite fascinating. I wonder if the architects understood what a half century of weathering would do to the surface.

[jgalt212]

Bummer, I thought Reginald Braithwaite was publishing again. When I first entered JavaScript world, I really enjoyed and benefited from his writing and talks.

[a4isms]

Here I am!

I still enjoy writing code like the code in TFA, but these days people seem a lot less interested in code than organizing their agentic LLMs, so I don't have the same incentive to share whatI find interesting. And it would be terrible marketing, like showing up to audition for a job driving F1... In a Jaguar E-Type.

Elegant and beautiful, but that isn't the game any more.

[firechickenbird]

The proof of non-regularity is a bit convoluted. You can easily apply the pumping lemma there

[Antibabelic]

What is some further reading y'all could recommend on formal languages?

[praptak]

That's what I learnt from as part of CS curriculum at MiMUW. Can recommend: https://en.wikipedia.org/wiki/Introduction_to_Automata_Theor...

[tehnub]

sipser's theory of computation