@Article{         AjtaiFagin:JSL:1990,
  Author        = "Ajtai, Miklos and Fagin, Ronald",
  Abstract      = {Although it is known that reachability in undirected finite graphs can be expressed by an existential monadic second-order sentence, our main result is that this is not the case for directed finite graphs (even in the presence of certain "built-in" relations, such as the successor relation). The proof makes use of Ehrenfeucht-Fraisse games, along with probabilistic arguments. However, we show that for directed finite graphs with degree at most k, reachability is expressible by an existential monadic second-order sentence.},
  date-added    = "2019-11-26 17:44:26 +0100",
  date-modified = "2019-11-26 17:56:46 +0100",
  ISSN          = "00224812",
  Journal       = "The Journal of Symbolic Logic",
  Number        = "1",
  Pages         = "113--150",
  Publisher     = "Association for Symbolic Logic",
  Title         = "Reachability is Harder for Directed Than for Undirected Finite Graphs",
  URL           = "http://www.jstor.org/stable/2274958",
  Volume        = "55",
  Year          = "1990",
  bdsk-url-1    = "http://www.jstor.org/stable/2274958",
  File          = "Reachability is Harder for Directed Than for Undirected Finite Graphs - 2274958 - a - a - u.pdf"
}

@Article{ AjtaiFagin:JSL:1990, Author = "Ajtai, Miklos and Fagin, Ronald", Abstract = {Although it is known that reachability in undirected finite graphs can be expressed by an existential monadic second-order sentence, our main result is that this is not the case for directed finite graphs (even in the presence of certain "built-in" relations, such as the successor relation). The proof makes use of Ehrenfeucht-Fraisse games, along with probabilistic arguments. However, we show that for directed finite graphs with degree at most k, reachability is expressible by an existential monadic second-order sentence.}, date-added = "2019-11-26 17:44:26 +0100", date-modified = "2019-11-26 17:56:46 +0100", ISSN = "00224812", Journal = "The Journal of Symbolic Logic", Number = "1", Pages = "113--150", Publisher = "Association for Symbolic Logic", Title = "Reachability is Harder for Directed Than for Undirected Finite Graphs", URL = "http://www.jstor.org/stable/2274958", Volume = "55", Year = "1990", bdsk-url-1 = "http://www.jstor.org/stable/2274958", File = "Reachability is Harder for Directed Than for Undirected Finite Graphs - 2274958 - a - a - u.pdf" }