Dofen Akuma – Is within 4 Amos of Kosher Sechach if there is non-Kosher Sechach in between:[1] If the wall is adjacent to invalid Sechach, then if it is within 4 Amos [188. cm[2], or 6.16 feet] of the Kosher Sechach [i.e. the non-Kosher Sechach takes up a space of less than 4 Amos], then the Sukkah remains Kosher as we apply the rule of Dofen Akuma. If the non-Kosher Sechach is more than 4 Amos wide and thus the wall is more than a four Ama distance from the Kosher Sechach, then the wall that is adjacent to the invalid Sechach is considered non-existent and can possibly invalidate the entire Sukkah if the Kosher Sechach will not remain with 3 Kosher walls. [The law of Dofen Akuma applies from all directions of the Sukkah, and hence it is possible to have less than 4 Amos of Sechach surrounding the Kosher Sechach from all 4 directions and the Sukkah still remain valid.[3] It is disputed amongst Poskim[4] whether the rule of Dofen Akum applies even if the wall of the Sukkah does not reach the invalid Sechach, and we thus must also apply the rule of Gud Asik. Practically, if the wall reaches within three Tefachim of the invalid Sechach then we apply the rule of Gud Asik and Dofen Akuma, and it remains valid.[5]]
[1] Michaber 632:1; See Piskeiy Teshuvos 632:3-4; 635:3
May two neighbors share the same Dofen Akuma? Yes. See Piskeiy Teshuvos 632:2
What is the law if there is a space of no Sechach directly adjacent to the invalid Sechach? If it is less than 3 Tefachim, the Sukkah remains Kosher. [Shut Rav Akiva Eigar 12] This applies even if in total the wall is more than 4 Amos distanced from the Kosher Sechach. [Bikureiy Yaakov 632:10; Piskeiy Teshuvos 632:3]
What is the law if the invalid Sechach is hovering above the Sukkah [i.e. a porch is hovering above the house wall of the Sukkah and is less than 4 Amos wide]? If there is valid Sechach in that area of the Sukkah, we apply the rule of Dofen Akuma, and certainly if there is invalid Sechach there, then it applies. If, however, there is nothing there, then it is disputed amongst Poskim if in such a case we apply the rule of Chavut Rami together with Dofen Akuma. [See Ashel Avraham Butcahch 632; Eretz Tzevi 48; Sdei Chemed 2:16; Piskeiy Teshuvos 632:23]
How to build the Sukkah when relying on Dofen Akuma for a wall: In such a case one is to first build the invalid Sechach near the wall, and only then build the valid Sechach. [Piskeiy Teshuvos 635:3]
[2] See Shiureiy Torah p. 249 that an Ama is 47 Dochakos [as opposed to 48 for a regular Tefach], by the Shiur Sukkah of 7×7 one should measure with the stringent approach of an Ama Sochakos, and the same would apply here Lechumra to measure the four Amos as Dochakos. See also M”B 633:2 and Shaar Hatziyon 633:2 that by Sukkah we follow the stringent approach in the dimensions, either Dochakos or Sochakos, and by the 7×7 dimension we follow Sochakos, and the same would apply here by the 20 Amos dimension; See also Midos Vishureiy Torah pp. 48-57 regarding Ama Sochakos and Dochakos; Piskeiy Teshuvos 633:1 writes that its 187.2 according to Grach Nah, when taking into account the Dochakos according to Chazon Ish, as he explains there in footnote 2
Other opinions-Chazon Ish: According to the Chazon Ish, the measurement is 226 cm following the 9.42 measurement of Tefach Dochakos. [See Piskeiy Teshuvos ibid]
[3] Michaber 632:2; Sukkah 4a
[4] See M”B 632:4 for a dispute on this matter; See Sukkah 4a which implies that we apply the rule of Dofen Akuma even when the wall does not reach the Sechach as the Talmud states that one can validate 20 cubic high Sukkah by making a ledge by the side which is within 4 cubits of the wall, and this ledge obviously does not reach the Sechach. Vetzaruch Iyun
[5] M”B ibid; See Piskeiy Teshuvos 632:3
Other opinions: Some Poskim rule that it is invalid even if it reaches within three Tefachim of the invalid Sechach. [Shut Rav Akiva Eigar 12, brought in Chazon Ish 77:7]