Flipsta library

The Flipsta library deals with finite-state automata. These are concise representations of, say, many word sequences, with probabilities attached to them. Many algorithms in text and speech processing can be expressed in terms of a handful of automaton operations.

The name “Flipsta” evokes rapid state changes. Also, it cleverly hides the acronym for “finite-state automaton” in plain view: Flipsta.

The source code is on GitHub.


The Flipsta library is licensed under the Apache License, Version 2.0.


Development of this library was funded by

  • EPSRC Project EP/I006583/1 (Generative Kernels and Score Spaces for Classification of Speech) within the Global Uncertainties Programme;
  • a Google Research Award.



Automata are directed graphs. The nodes represent states, and the edges transitions, which will be called “arcs” for short. On the arcs are labels, which can be symbol sequences, numerical weights, a product of various weights, or other things. They must, however, be in a semiring.

An example automaton, which could represent the output of a speech recogniser, is:


It has state A, B, C, and D. The circle of state A is in bold, which indicates a start state. State B has a double line, which indicates a final state. This automaton probably represents the sequences

  • a a c with probability ⅛.
  • a c c with probability ⅜.
  • b a c with probability ⅛.
  • b c c with probability ⅜.

The overall probability has been assumed to be the product of the weights, but this could have been different. The interpretation of these operation depends on the semiring that they are in. In brief, a semiring defines an operation ⊗ which is applied to merge consecutive labels while traversing the automaton. Here, ⊗ is defined as ×, normal times, so it just multiplies the weights. (A semiring also defines an operation ⊕ that is applied to merge competing paths, but that is not used in this example.)

Incidentally, it is not just the weights that must be in a semiring, but also the symbol sequences. Each of the symbols a, b, and c is a one-symbol sequence, and the operation ⊗ is defined as concatenating two sequences. (The operation ⊕ is less easy to define.) Thus, (b, ½) ⊗ (a, ¼) = (b a, ⅛), and (b a, ⅛) ⊗ (c, 1) = (b a c, ⅛), which is the label for one complete path.

The flexibility of the Flipsta library, compared to other libraries that deal with finite-state automata, derives in large part from its extreme view on the labels on the transitions between states of automata. Other libraries fix the number of symbol sequences to 1 (to get finite-state acceptors) or 2 (to get finite-state transducers), and zero or one weight. Through these are fine choices for many applications, many require an n-tape automaton with n>2. Whole papers are written about how to do this. Indeed, the OpenFst library allows users to work around the 2-tape restriction by moving extra symbols into the weights. (They then become awkward to manipulate.)

The Flipsta library circumvents this by allowing only one label, which must be in a semiring, but by allowing it to be composite. Though C++11 variadic templates (and elaborate machinery underneath that manipulates the types), any combination and number of symbols and more traditional (or more outlandish) semirings can be used as labels. Three-tape automata are thus just one line of code away.

Other libraries

Other libraries that deal with finite-state automata are:

Previous topic

Flipsta library

Next topic

Using the Flipsta library

This Page