Blog post automata

_data/authors.yml

@@ -88,3 +88,17 @@ Patrick J. Roddy:
     - label: Website
       icon: fas fa-fw fa-link
       url: https://paddyroddy.github.io
+Eliot W. Robson:
+  name        : Eliot W. Robson
+  bio         : "PhD Student, University of Illinois Urbana-Champaign"
+  avatar      : /images/people/eliot-w-robson.jpg
+  links:
+    - label: "Email"
+      icon: "fas fa-fw fa-envelope-square"
+      url: "mailto:[email protected]"
+    - label: GitHub
+      icon: fab fa-fw fa-github
+      url: https://github.com/eliotwrobson
+    - label: LinkedIn
+      icon: fab fa-fw fa-linkedin
+      url: https://www.linkedin.com/in/eliot-robson/

_posts/2024-07-10-automata.md

@@ -0,0 +1,126 @@
+---
+layout: single
+title: "automata: Simulation and manipulation"
+excerpt: automata is a package implementing structures and algorithms for manipulating finite automata, pushdown automata, and Turing machines, that was recently accepted into the pyOpenSci ecosystem.
+author: Eliot W. Robson
+permalink: /blog/automata
+header:
+    overlay_image: /images/automata/finite_language_dfa.png
+    overlay_filter: rgba(20, 13, 36, 0.8)
+categories:
+  - blog-post
+  - automata
+  - formal-languages
+  - models-of-computation
+  - pyos-accepted
+classes: wide
+comments: true
+---
+
+
+Automata are abstract machines used to represent models of computation, and are a central object of study in theoretical computer science. Given an input string of characters over a fixed alphabet, these machines either accept or reject the string. A language corresponding to an automaton is
+the set of all strings it accepts. Three important families of automata in increasing order of generality are the following:
+
+1. Finite-state automata
+2. Pushdown automata
+3. Turing machines
+
+The [`automata`](https://caleb531.github.io/automata/) package facilitates working with these families by allowing simulation of reading input and higher-level manipulation
+of the corresponding languages using specialized algorithms. For an overview on automata theory, see [this Wikipedia article](https://en.wikipedia.org/wiki/Automata_theory), and
+for a more comprehensive introduction to each of these topics, see [these lecture notes](https://jeffe.cs.illinois.edu/teaching/algorithms/#models).
+
+## Statement of need
+
+Automata are a core component of both computer science education and research, seeing further theoretical work
+and applications in a wide variety of areas such as computational biology and networking.
+Consequently, the manipulation of automata with software packages has seen significant attention from
+researchers in the past. The similarly named Mathematica package [`Automata`](https://www.cs.cmu.edu/~sutner/automata.html) implements a number of
+algorithms for use with finite-state automata, including regular expression conversion and binary set operations.
+In Java, the [Brics package](https://www.brics.dk/automaton/) implements similar algorithms, while the [JFLAP package](https://www.jflap.org/) places an emphasis
+on interactivity and simulation of more general families of automata.
+
+[`automata`](https://caleb531.github.io/automata/) serves the demand for such a package in the Python software ecosystem, implementing algorithms and allowing for
+simulation of automata in a manner comparable to the packages described previously. As a popular high-level language, Python enables
+significant flexibility and ease of use that directly benefits many users. The package includes a comprehensive test suite,
+support for modern language features (including type annotations), and has a large number of different automata,
+meeting the demands of users across a wide variety of use cases. In particular, the target audience
+is both researchers that wish to manipulate automata, and for those in educational contexts to reinforce understanding about how these
+models of computation function.
+
+## Package features
+
+The API of the package is designed to mimic the formal mathematical description of each automaton using built-in Python data structures
+(such as sets and dicts). This is for ease of use by those that are unfamiliar with these models of computation, while also providing performance
+suitable for tasks arising in research. In particular, algorithms in the package have been written for tackling
+performance on large inputs, incorporating optimizations such as only exploring the reachable set of states
+in the construction of a new finite-state automaton. The package also has native display integration with Jupyter
+notebooks, enabling easy visualization that allows students to interact with [`automata`](https://caleb531.github.io/automata/) in an exploratory manner.
+
+Of note are some commonly used and technical algorithms implemented in the package for finite-state automata:
+
+- An optimized version of the Hopcroft-Karp algorithm to determine whether two deterministic finite automata (DFA) are equivalent.
+
+- The product construction algorithm for binary set operations (union, intersection, etc.) on the languages corresponding to two input DFAs.
+
+- Thompson's algorithm for converting regular expressions to equivalent nondeterministic finite automata (NFA).
+
+- Hopcroft's algorithm for DFA minimization.
+
+- A specialized algorithm for directly constructing a state-minimal DFA accepting a given finite language.
+
+- A specialized algorithm for directly constructing a minimal DFA recognizing strings containing a given substring.
+
+To the authors' knowledge, this is the only Python package implementing all of the automata manipulation algorithms stated above.
+
+## Example usage
+
+![A visualization of `target_words_dfa`. Transitions on characters leading to immediate rejections are omitted.]({{ site.url }}/images/automata/finite_language_dfa.png)
+
+The following example is inspired by the use case described in [this blog post](http://blog.notdot.net/2010/07/Damn-Cool-Algorithms-Levenshtein-Automata).
+We wish to determine which strings in a given set are within the target edit distance
+to a reference string. We will first initialize a DFA corresponding to a fixed set of target words
+over the alphabet of all lowercase ascii characters.
+
+```python
+from automata.fa.dfa import DFA
+from automata.fa.nfa import NFA
+import string
+
+target_words_dfa = DFA.from_finite_language(
+  input_symbols=set(string.ascii_lowercase),
+  language={'these', 'are', 'target', 'words', 'them', 'those'},
+)
+```
+
+Next, we construct an NFA recognizing all strings within a target edit distance of a fixed
+reference string, and then immediately convert this to an equivalent DFA. The package provides
+builtin functions to make this construction easy, and we use the same alphabet as the DFA that was just created.
+
+```python
+words_within_edit_distance_dfa = DFA.from_nfa(
+  NFA.edit_distance(
+    input_symbols=set(string.ascii_lowercase),
+    reference_str='they',
+    max_edit_distance=2,
+  )
+)
+```
+
+Finally, we take the intersection of the two DFAs we have constructed and read all of
+the words in the output DFA into a list. The library makes this straightforward and idiomatic.
+
+```python
+found_words_dfa = target_words_dfa & words_within_edit_distance_dfa
+found_words = list(found_words_dfa)
+```
+
+The DFA `found_words_dfa` accepts strings in the intersection of the languages of the
+DFAs given as input, and `found_words` is a list containing this language. Note the power of this
+technique is that the DFA `words_within_edit_distance_dfa`
+has an infinite language, meaning we could not do this same computation just using the builtin
+sets in Python directly (as they always represent a finite collection), although the
+syntax used by [`automata`](https://caleb531.github.io/automata/) is very similar to promote intuition.
+
+## Citing
+
+This post is adapted from [our JOSS paper](https://joss.theoj.org/papers/10.21105/joss.05759), which should be used for citations.