super mario bros. is np-hard
TRANSCRIPT
Super Mario Bros. is NP-Hard[Aloupis, Demaine, Guo, Viglietta 2014]
π₯π₯ OR Β¬π¦π¦ OR π§π§ & π₯π₯ OR π¦π¦ OR Β¬π¦π¦ &(Β¬π₯π₯ OR Β¬π¦π¦ OR Β¬π§π§) & (Β¬π₯π₯ OR Β¬π¦π¦ OR Β¬π§π§)
[Bern & Hayes 1996]
Akari / Light Up [Nikoli 2001]
Akari / Light Up is NP-complete[McPhail 2005]
wire gadget
Akari / Light Up is NP-complete[McPhail 2005]
split/negationgadget
Akari / Light Up is NP-complete[McPhail 2005]
split gadget NOT gate
Akari / Light Up is NP-complete[McPhail 2005]
OR/XNOR gate
crossover gadget
Akari / Light Up is NP-complete[McPhail 2005]
Β¬π₯π₯ β¨ π₯π₯ β§ π¦π¦ β¨ π§π§
π₯π₯
π₯π₯ π₯π₯
π₯π₯π₯π₯β²
π₯π₯β²
π§π§
π§π§
π₯π₯β²π₯π₯
π¦π¦β²
π¦π¦
π¦π¦
β¨
β§
β¨
π₯π₯
π₯π₯
Minesweeper Consistency isNP-complete [Kaye 2000]
wire
wire terminator
split,NOT,turn
π₯π₯π₯π₯ π₯π₯π₯π₯ π₯π₯π₯π₯ π₯π₯π₯π₯ π₯π₯π₯π₯ π₯π₯π₯π₯π₯π₯π₯π₯ π₯π₯π₯π₯
π₯π₯π₯π₯ π₯π₯ π₯π₯
π₯π₯π₯π₯
π₯π₯π₯π₯
π₯π₯π₯π₯π₯π₯π₯π₯
π₯π₯ π₯π₯
π₯π₯π₯π₯π₯π₯
Minesweeper Consistency isNP-complete [Kaye 2000]
NOT
Phase changer(2 NOTs)
π₯π₯ π₯π₯π₯π₯ π₯π₯ π₯π₯π₯π₯ π₯π₯π₯π₯π₯π₯
π₯π₯π₯π₯ π₯π₯π₯π₯π₯π₯ π₯π₯ π₯π₯π₯π₯ π₯π₯π₯π₯
π₯π₯ π₯π₯
π₯π₯ π₯π₯
Minesweeper Consistency isNP-complete [Kaye 2000]
AND
turn
π₯π₯π₯π₯π₯π₯
π₯π₯
π₯π₯π₯π₯
π₯π₯
π§π§
π₯π₯π₯π₯
π₯π₯
π₯π₯
π§π§π§π§
π§π§
π§π§π§π§ π§π§
π₯π₯ π₯π₯π‘π‘ π‘π‘ π‘π‘ π‘π‘ π‘π‘ π‘π‘ π‘π‘ π‘π‘π‘π‘ π‘π‘
π‘π‘
π‘π‘
π‘π‘
π‘π‘
Minesweeper Consistency isNP-complete [Kaye 2000]
crossover
XOR
[Goldschlager 1977]
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
turn gadgetwire gadget terminator gadget
π₯π₯ π₯π₯
π₯π₯
π₯π₯
π₯π₯ π₯π₯
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
OR gate
NOT gate shifter gadget
π₯π₯ π₯π₯π₯π₯ π₯π₯
π₯π₯ π₯π₯ π₯π₯ π₯π₯ π₯π₯ π₯π₯ π₯π₯ π₯π₯ π₯π₯
π₯π₯ π₯π₯ π₯π₯ π₯π₯ π₯π₯
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
split gadget
crossover gadget
NOT
shiftershifter
π₯π₯ π₯π₯ π₯π₯ π₯π₯π₯π₯ π₯π₯π₯π₯
π₯π₯π₯π₯
π₯π₯
π₯π₯ π₯π₯ π₯π₯ π₯π₯
π₯π₯ π₯π₯
π£π£
π£π£π£π£
π£π£π£π£
π£π£π£π£
π£π£
π₯π₯ π₯π₯
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
NAND
alternative crossover
gadget
Minesweeper is CoNP-Complete[Scott, Stege, van Rooij 2011]
Functionally Complete Logic Gates
[Wernick 1942]
Candy Crush is NP-complete[Walsh 2014]
variablegadget
true
false
Candy Crush is NP-complete[Walsh 2014]
connectorgadgets
positive
negative
out
out
Candy Crush is NP-complete[Walsh 2014]
wiregadget
out
out
in
in
Candy Crush is NP-complete[Walsh 2014]
out
out
in
in
modifiedwire
gadget
Candy Crush is NP-complete[Walsh 2014]
out
out
in
in
modifiedwire
gadget
Candy Crush is NP-complete[Walsh 2014]
out
out
in
in
modifiedwire
gadget
Candy Crush is NP-complete[Walsh 2014]
π₯π₯1
clausegadget
π₯π₯1
π₯π₯2
π₯π₯2
π₯π₯3
π₯π₯3
rewardgadget
Bejeweled, Candy Crush, β¦ areNP-Complete [Guala, Leucci, Natale 2014]
Bejeweled, Candy Crush, β¦ areNP-Complete [Guala, Leucci, Natale 2014]