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'The Polynomial - Space of the music' has to been taken literally. Fieldrunners is a Tower Defense game for the iPhone. My Rating: The Polynomial: Space of the Music (2010) (2.12 average Grouvee user rating). An intense keyboard and mouse side-scrolling shooter developed by Crack Dot Com. Algoriddim GmbH. AmpliTube for iPad. Polynomial's songs: Listen to songs by Polynomial on Myspace, Stream Free Online Music by Polynomial.
- 'The Polynomial - Space of the music' has to been taken literally. Fieldrunners is a Tower Defense game for the iPhone. My Rating: The Polynomial: Space of the Music (2010) (2.12 average Grouvee user rating). An intense keyboard and mouse side-scrolling shooter developed by Crack Dot Com. Algoriddim GmbH. AmpliTube for iPad.
- Neon Bible: The Polynomial, Demo. Quintin Smith. 10 years ago. 56 RPS's own Lewie Proctor tipped us off about this. The Polynomial: Space of the Music is a shooter out now on Steam, boasting a demo, a reasonable £5.99 pricetag and the prettiest screenshots in the world.Lured by these magnificent images, Jim and I had a play.
The Polynomial is a trippy and intriguing voyage through space.
![Crack Crack](/uploads/1/2/9/4/129460352/550780991.jpg)
Trying to figure out exactly what you’re meant to be doing in The Polynomial – Space of the Music is a game in itself. Set in a universe created based on whatever music is currently playing, you’re not given any real objective as such. It’s more a case of floating around, attacking anything that shoots in your direction, and exploring this weird, trippy world.
Being able to import your own music into the game and listen to custom playlists while you navigate the gorgeous environments is a great touch, and there are plenty of effects to mess around and sliders to experiment with. Unfortunately, the ‘make your own journey’ angle is a rather double-edged sword, as you’ll lost interest pretty quickly when you feel that you’ve seen everything.
The Polynomial throws you into a space arena, with colourful stars and lights illuminating your surroundings. Everything looks so beautiful, with sweeping rows of light against a dark background, and trippy abstract creatures moving about the place. You’re given a quick introduction to the controls, then let loose into the big, bad world.
Basic gameplay ideas form slowly as you being to explore. Left-clicking fires a stream of lasers, and you’ll encounter baddies that look like evil Chain Chomps from the Mario games. These guys will spray you with bullet fire, but hit them back enough and they’ll explode with a satisfyingly bright aura.
There are also strange, squiggly lines floating about the place, and it turns out these are your allies who need saving from the nasty chompers. Collecting power-ups and flying through wormholes will increase your power and allow you to progress. It’s all relatively simple, yet it’s hard to shake the feeling that there is more to this game than meets the eye.
Worlds are generated depending on what music you play. Any mp3 tracks from your computer can be used, and playlists can be set up – although these cannot be saved, and must be created each time you boot up the game. There isn’t really a noticeable difference when changing the current track, but it’s still nice to be able to listen to your own music while exploring.
You’ll most likely spend just as much time in the menus as you will flying around space, as there are tons of editing options available. It’s possible to alter the lighting effects, the number of stars, the visual effects, and even go as far as to change specific co-ordinates, although the majority of players will most likely feel overwhelmed by all these intricate details and leave this well alone.
While The Polynomial is definitely an intriguing project, it feels like more of a tech demo than an actual game. There are online high-score boards for those who like to track their shooting skills, but looking past the pretty visuals, there really isn’t all that much to do. Within an hour, you’ll most likely feel that you’ve seen everything the game has to offer.
With a bit more direction and purpose, The Polynomial could very well be an essential musical mind-trip, but in its current form there just isn’t enough to see and do past the ‘ooh so pretty’ initial reactions. Still, it’s definitely worth downloading the demo and experiencing it for yourself.
(Redirected from Polynomial space)
Unsolved problem in computer science: (more unsolved problems in computer science) |
In computational complexity theory, PSPACE is the set of all decision problems that can be solved by a Turing machine using a polynomialamount of space.
Formal definition[edit]
If we denote by SPACE(t(n)), the set of all problems that can be solved by Turing machines using O(t(n)) space for some function t of the input size n, then we can define PSPACE formally as[1]
PSPACE is a strict superset of the set of context-sensitive languages.
It turns out that allowing the Turing machine to be nondeterministic does not add any extra power. Because of Savitch's theorem,[2] NPSPACE is equivalent to PSPACE, essentially because a deterministic Turing machine can simulate a non-deterministic Turing machine without needing much more space (even though it may use much more time).[3] Also, the complements of all problems in PSPACE are also in PSPACE, meaning that co-PSPACE = PSPACE.
Relation among other classes[edit]
A representation of the relation among complexity classes
The following relations are known between PSPACE and the complexity classes NL, P, NP, PH, EXPTIME and EXPSPACE (note that ⊊, meaning strict containment, is not the same as ⊈):
It is known that in the first and second line, at least one of the set containments must be strict, but it is not known which. It is widely suspected that all are strict.
The containments in the third line are both known to be strict. The first follows from direct diagonalization (the space hierarchy theorem, NL ⊊ NPSPACE) and the fact that PSPACE = NPSPACE via Savitch's theorem. The second follows simply from the space hierarchy theorem.
The hardest problems in PSPACE are the PSPACE-complete problems. See PSPACE-complete for examples of problems that are suspected to be in PSPACE but not in NP.
Closure properties[edit]
The class PSPACE is closed under operations union, complementation, and Kleene star.
The Polynomial - Space Of The Music Crack Key
Other characterizations[edit]
An alternative characterization of PSPACE is the set of problems decidable by an alternating Turing machine in polynomial time, sometimes called APTIME or just AP.[4]
A logical characterization of PSPACE from descriptive complexity theory is that it is the set of problems expressible in second-order logic with the addition of a transitive closure operator. A full transitive closure is not needed; a commutative transitive closure and even weaker forms suffice. It is the addition of this operator that (possibly) distinguishes PSPACE from PH.
A major result of complexity theory is that PSPACE can be characterized as all the languages recognizable by a particular interactive proof system, the one defining the class IP. In this system, there is an all-powerful prover trying to convince a randomized polynomial-time verifier that a string is in the language. It should be able to convince the verifier with high probability if the string is in the language, but should not be able to convince it except with low probability if the string is not in the language.
PSPACE can be characterized as the quantum complexity class QIP.[5]
PSPACE is also equal to PCTC, problems solvable by classical computers using closed timelike curves,[6] as well as to BQPCTC, problems solvable by quantum computers using closed timelike curves.[7]
PSPACE-completeness[edit]
A language B is PSPACE-complete if it is in PSPACE and it is PSPACE-hard, which means for all A ∈ PSPACE, , where means that there is a polynomial-time many-one reduction from A to B. PSPACE-complete problems are of great importance to studying PSPACE problems because they represent the most difficult problems in PSPACE. Finding a simple solution to a PSPACE-complete problem would mean we have a simple solution to all other problems in PSPACE because all PSPACE problems could be reduced to a PSPACE-complete problem.[8]
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An example of a PSPACE-complete problem is the quantified Boolean formula problem (usually abbreviated to QBF or TQBF; the T stands for 'true').[8]
References[edit]
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- ^Arora & Barak (2009) p.81
- ^Arora & Barak (2009) p.85
- ^Arora & Barak (2009) p.86
- ^Arora & Barak (2009) p.100
- ^Rahul Jain; Zhengfeng Ji; Sarvagya Upadhyay; John Watrous (July 2009). 'QIP = PSPACE'. arXiv:0907.4737.
- ^S. Aaronson (March 2005). 'NP-complete problems and physical reality'. SIGACT News. arXiv:quant-ph/0502072. Bibcode:2005quant.ph..2072A..
- ^Watrous, John; Aaronson, Scott (2009). 'Closed timelike curves make quantum and classical computing equivalent'. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 465 (2102): 631. arXiv:0808.2669. Bibcode:2009RSPSA.465..631A. doi:10.1098/rspa.2008.0350.
- ^ abArora & Barak (2009) p.83
- Arora, Sanjeev; Barak, Boaz (2009). Computational complexity. A modern approach. Cambridge University Press. ISBN978-0-521-42426-4. Zbl1193.68112.
- Sipser, Michael (1997). Introduction to the Theory of Computation. PWS Publishing. ISBN0-534-94728-X. Section 8.2–8.3 (The Class PSPACE, PSPACE-completeness), pp. 281–294.
- Papadimitriou, Christos (1993). Computational Complexity (1st ed.). Addison Wesley. ISBN0-201-53082-1. Chapter 19: Polynomial space, pp. 455–490.
- Sipser, Michael (2006). Introduction to the Theory of Computation (2nd ed.). Thomson Course Technology. ISBN0-534-95097-3. Chapter 8: Space Complexity
- Complexity Zoo: PSPACE
The Polynomial - Space Of The Music Crack Pdf
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