なしに

1. 1Without N; doing something while N is absent or not done.
2. 2Followed by a negative: without N (a necessary condition), the result is impossible.Ex. 1
3. 3Without N, an action or access is not allowed or possible.Ex. 2

A somewhat formal expression, common in writing, speeches and explanations. It frequently appears in the frame 'N なしに…ない' to present N as indispensable. The variant なしで is more common in casual speech. Verbs use ことなしに, and 抜きで/抜きにして is preferred for deliberately leaving something out.

• ことなしにN1「ことなしに」attaches to the dictionary form of a verb, while 「なしに」attaches only to nouns; their meanings basically match, so switch to 「ことなしに」when a verb is involved. That said, 「ことなしに」is stiff written language, so for everyday small matters prefer 「ずに」or「ないで」.
• なくしてN1「なくして」covers only the necessary-condition sense of 「なしに」, and in that sense the two are interchangeable, with the following clause required to be negative, impossible, or difficult. It is more formal and literary than 「なしに」and often carries an emotional tone, but the 'did X without doing Y' sense cannot take 「なくして」.
• ことなくN2「ことなく」attaches to the dictionary form of a verb, as in 「休むことなく」, and is more literary than 「なしに」. It often pairs with 「一度も」and stresses that something that could have happened never did.
• ずにN3「ずに」attaches to verbs (「する」→「せずに」), while 「なしに」attaches only to nouns. For the 'did X without doing Y' meaning the two can swap, as in 「断りなしに」≈「断らずに」; for necessary conditions, use 「noun + なしには」and「verb + ずには」followed by a negative, respectively.
• ないでN3「ないで」attaches to the ない-form of a verb and sounds plain and neutral. In the 'did X without doing Y' sense it is close to 「なしに」, as in 「断りなしに」≈「断らないで」, and it can also express 'instead of' and make end-of-sentence requests — two uses 「なしに」lacks.
• 抜きで / 抜きにしてN2「抜きで」focuses on leaving out a person or thing that would normally be included, and 「を」can be added after the noun. Deliberate-omission phrasings like 「前置きは抜きにして」cannot be replaced with 「なしに」, though for necessary conditions 「を抜きにしては」is close to 「なしには」.

なしに follows nouns, while ことなしに, ことなく, ずに and ないで follow verbs (ずに and ないで being everyday forms). なくして is a more formal, literary way of stressing an indispensable condition, and 抜きで / 抜きにして stress intentionally omitting something normally included.