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"Do not sit on fence" and "Do not slam door" are examples of telegraphic speech. Telegraphic expressions are commonly used as newspaper headlines, as bulleted lists in presentations, on signs or any other place where brevity may be desired. In other words, leaving out small words (like "the", "a", and so on) saves space.
Here's more:
"A telegraphic expression is speech that is limited in meaning and produced without inflections or function words. Function words, also called closed-class words, can include determiners such as "a" and "the" and demonstratives such as "this" or "that". Other closed-class words can include pronouns, except for nominative case pronouns such as "he" and "she", auxiliary verbs such as "have", "be", "will", and auxiliary verb derivatives. Closed-class words serve the functional purpose of tying open-class words, called content words, together. For example, the closed-class words within the grammatical text phrase, "the boy has pushed the girl", are "the", and "has". By removing these closed-class words, the resulting text, "boy pushed girl" is said to be a telegraphic expression. Notably, closed-class words, such as demonstratives and pronouns, typically are comprised of a limited number of members. Such words are said to be closed-class words because new functional words are rarely added to a language. Accordingly, the number of closed-class words remains fairly constant."
Source 
Articles in negative sentences 
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