Without (classical form): 〜なき

なき is the classical form of ない before a noun: 罪なき人々 = 罪のない人々 (innocent people). It gives a literary, grave or poetic tone, and appears in many fixed expressions: 名もなき花, 飽くなき探求, 声なき声. Written, literary register.

• 戦争で多くの罪なき人々が犠牲になった。せんそうでおおくのつみなきひとびとがぎせいになった。The war claimed many innocent victims.
• 名もなき花が、道ばたにひっそりと咲いている。なもなきはなが、みちばたにひっそりとさいている。A nameless flower blooms quietly by the roadside.
• 彼の飽くなき探求心には、誰もが感心する。かれのあくなきたんきゅうしんには、だれもがかんしんする。Everyone admires his insatiable spirit of inquiry.

In classical Japanese, the adjective なし (“not to exist”) took the form なき before a noun. Modern Japanese says ない (罪のない人), but なき has survived in written, formal language, where it brings gravity and poetry — rather like English “-less” in words such as “nameless”, “ceaseless”.

Note: with なき, you drop the の of modern Japanese. 罪のない人 becomes 罪なき人.

• 希望なき時代にも、人々は歌を歌い続けた。きぼうなきじだいにも、ひとびとはうたをうたいつづけた。Even in times without hope, people never stopped singing.

Noun + なき + noun. With も, it's more emphatic: 名もなき (“without so much as a name”). After a verb in the dictionary form, a few fixed expressions exist (飽くなき, “unwearying”). The classical conditional なかりせば (“had there not been”) can still be read in formal texts.

• 彼の助けなかりせば、この計画は成功しなかっただろう。かれのたすけなかりせば、このけいかくはせいこうしなかっただろう。Had it not been for his help, this project would probably not have succeeded.
• 政治家は、声なき声にこそ耳を傾けるべきだ。せいじかは、こえなきこえにこそみみをかたむけるべきだ。Politicians should listen above all to those who have no voice.

〜のない is the neutral modern form (罪のない人). 〜なしの is used for a concrete lack, often in practical life (連絡なしの欠席, 砂糖なしのコーヒー). 〜なき is literary. Watch out for the homophone 亡き (late, deceased): 亡き父 = my late father, which has nothing to do with the absence of something.

• 連絡なしの欠席は認められない。れんらくなしのけっせきはみとめられない。Absences without notice are not accepted. (なしの, practical)
• 亡き母の手紙を読み返した。なきははのてがみをよみかえした。I reread my late mother's letters. (亡き = late, deceased)