Finite state automata (FSA), also known as finite state machines (FSM), are usually classified as being deterministic (DFA) or non-deterministic (NFA). A deterministic finite state automaton has exactly one transition from every state for each possible input. In other words, whatever state the FSA is in, if it encounters a symbol for which a transition exists, there will be just one transition and obviously as a result, one follow up state. For a given string, the path through a DFA is deterministic since there is no place along the way where the machine would have to choose between more than one transition.  Given this definition it isn’t too hard to figure out what an NFA is. Unlike in DFA, it is possible for states in an NFA to have more than one transition per input symbol. Additionally, states in an NFA may have states that don’t require an input symbol at all, transitioning on the empty string ε.

Superficially it would appear that deterministic and non-deterministic finite state automata are entirely separate beasts. It turns out, however, that they are equivalent. For any language recognized by an NFA, there exists a DFA that recognizes that language and vice versa. The algorithm to make the conversion from NFA to DFA is relatively simple, even if the resulting DFA is considerably more complex than the original NFA.  After the jump I will prove this equivalence and also step through a short example of converting an NFA to an equivalent DFA.

In my last post, “Kleene’s Theorem,” I provided some useful background information about strings, regular languages, regular expressions, and finite automata before introducing the eponymously named theorem that has become one of the cornerstones of artificial intelligence and more specifically, natural language processing (NLP).  Kleene’s Theorem tells us that regular expressions and finite state automata are one and the same when it comes to describing regular languages. In the post I will provide a proof of this groundbreaking principle.

Stephen Kleene

Stephen Cole Kleene was an American mathematician who’s groundbreaking work in the sub-field of logic known as recursion theory laid the groundwork for modern computing.  While most computer programmers might not know his name or the significance of his work regarding computable functions, I am willing to bet that anyone who has ever dealt with regular expressions is intimately familiar with an indispensable operator that resulted directly from his work and even bears his name, the *, or as it is formally known, the Kleene star.

While his contributions to computer science in general cannot be overstated, Kleene also authored a theorem that plays an important role in artificial intelligence, specifically the branch known as natural language processing, or NLP for short. Kleene’s Theorem relates regular languages, regular expressions, and finite state automata (FSAs). In short, he was able to prove that regular expressions and finite state automata were the same thing, just two different representations of any given regular language.

From Vienna Bienalle 2017, taking place this week in Austria, comes a new take on Isaac Asimov’s Three Laws of Robotics.  The head of the project, Christoph Thun-Hohenstein, says the update was necessitated by:

…the need for benign intelligent robots and the necessity of cultivating a culture of quality committed to serving the common good!

That sounds a lot like Asimov’s reasoning, but the new laws are certainly worthy of consideration and debate.

Boston Dynamics, the MIT spin-off and self-proclaimed maker of “nightmare-inducing robots“, has been sold by its parent company Alphabet (aka Google) to the Japanese tech behemoth SoftBank. No specifics regarding the price or the terms of the sale have been announced which is not surprising given we still don’t know how much Google paid for the company when it purchased it four years ago.

I know that this post will probably be of interest to about a dozen people worldwide, and even those few may be disappointed by it. Since the official SWI-Prolog packages aren’t often kept up to date and because compiling and installing SWI-Prolog from source should be both quick and straightforward, that is the recommended way to do it on Linux and other *nix systems.

If you are looking for tips, tricks or assistance with an installation problem, you likely won’t find it here. The instructions provided on the SWI-Prolog site for building and installing SWI-Prolog from source code “just worked” for me. Nevertheless, I want to document what I did, and if you are looking for the Cliff Notes version, then by all means, read on.

Set 38 years in the future, the plot of 2002’s blockbuster film Minority Report revolves around Washington DC’s PreCrime unit, a police force who able to stop future murders from happening with the aid of three mutant human who are able to predict homicides before they happen.  Minority Report managed to side step the “psychic predicts a murder” cliché storyline with its innovative use of technology: not only could precogs predict future murders, but their visions could be streamed via a neural bridge in the form of a video that the police officers could watch. Fantastical? Nope, and researchers from MIT already have a jump on the technology.