Dec 07 2017

Day 7 – First Order Stormtrooper

I’ll be the first to admit that I am no military strategist, but if the First Order wants to have any shot of winning this thing, they really should arm their soldiers. Day 7 of the LEGO Star Wars Advent calendar is a First Order Stormtrooper – a weaponless First Order Stormtrooper. I’ll let it slide. Given my previous experience with these calendars it’s a safe bet that’s there’s a cache of weapons forthcoming.

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Dec 06 2017

Day 6 – First Order Transporter

LEGO calls this a Stormtrooper Transport, which I guess it is, but since these weren’t around until The Force Awakens it is technically a First Order Transporter or Atmospheric Assault Lander if you’re nasty. I admit to finding this build challenging, even thinking at one point that all of the pieces weren’t included. I also admit to not having any coffee before tackling it so ymmv.

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Dec 05 2017

Day 5 – Resistance Officer

Resistance Officer Minifigure

I have mixed feelings about today’s offering. It is a Resistance officer minifigure, and I generally like all minifigures. But it’s also about as generic as a minifigure can be. I don’t remember leaving the theater after The Force Awakens and talking with my daughter about how awesome the Resistance officers were. But then again he does have the same haircut as me. I guess I ultimately lean toward liking it but only by a hair.

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Dec 04 2017

Day 4 – Blaster Cannon

Finally a build not from Rebels. Well, it’s not from Rebels per se because Day 4’s blaster cannon is generic enough that it could have been from any Star Wars movie or animated series. I remember seeing the the Snowtroopers lugging and setting up one of these when they assaulted the rebel base on Hoth, so I’m going to say it’s from The Empire Strikes Back. Yay! The Advent calendar gave us one from the original trilogy, and the best movie from the entire series by far.

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Dec 03 2017

Day 3 – The Phantom

I’m beginning to think that it might be Rebels all the way down. It’s day 4 of the LEGO Star Wars Advent calendar, and we’ve got another spaceship from the animated series Rebels. Although it was eventually lost over the gas planet of Yarma, the modified VCX-series auxiliary starfighter known as the Phantom served Ezra Bridger and his crewmates of the Phantom’s mothership, the Ghost, well during the early days of the rebellion. I’m pleased to have built the Phantom since you really can’t have the Ghost without the Phantom (or the Phantom II now) even if today’s build is not the same scale as the Ghost from Day 1.

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Dec 02 2017

Necessity and Sufficiency

Necessity - Sufficient Venn DiagramAm I sufficient? Am I even necessary? If you’re plagued by these existential questions and have ended up here in your quest for an answer, then I’ve got some bad news for you. The answer to both is no. I keed. I keed. Actually, the bad news is that this post is about necessity and sufficiency and their rigid definitions in the domain of mathematical logic. If you are only interested in looking for meaning in your life then move along, but if you are one of the enlightened few that knows that math really is the answer to every question, then by all means, read on!

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Dec 02 2017

Day 2 – Sabine Wren

Day 2 of the LEGO Star Wars Advent calendar is keeping it Rebels, and that is more than ok with me. Minifigures are my favorite, and Mandalorian warrior turned rebel Sabine Wren is a new one for my collection.

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Dec 01 2017

Day 1 – The Ghost

Day 1 is finally here, and it was well worth the wait. The first build from the 2017 LEGO Star Wars Calendar is a mini version of The Ghost from the animated series Rebels. Piloted by Hera Syndulla, The Ghost has, in the three short years of the cartoon’s, run become as iconic as any other in the Star Wars universe.

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Nov 30 2017

Day 0 – Inside the Box

23 long days I’ve waited to open this box up, and in less than 20 hours I will find out what’s behind door # 1. For now my appetite has been whetted by the calendar’s backdrop: Starkiller Base hovering over a Jakku littered with Star Destroyers, AT-ATs, and Christmas trees.  That’s not quite how I remember The Force Awakens, but for LEGO Star Wars I’ll let it slide.

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Nov 26 2017

NFA and DFA Equivalence Theorem Proof and Example

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.

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