Decision Procedures for Path Feasibility of String-Manipulating Programs with Complex Operations
In this paper we provide two general semantic conditions which together ensure the decidability of path feasibility: (1) each assertion admits regular monadic decomposition (i.e. is an effectively recognisable relation), and (2) each assignment uses a (possibly nondeterministic) function whose inverse relation preserves regularity. We show that the semantic conditions are expressive since they are satisfied by a multitude of string operations including concatenation, one-way and two-way finite-state transducers, replace-all functions (where the replacement string could contain variables), string-reverse functions, regular-expression matching, and some (restricted) forms of letter-counting/length functions. The semantic conditions also strictly subsume existing decidable string theories (e.g. straight-line fragments, and acyclic logics), and most existing benchmarks (e.g. most of Kaluza’s, and all of SLOG’s, Stranger’s, and SLOTH’s benchmarks). Our semantic conditions also yield a conceptually simple decision procedure, as well as an extensible architecture of a string solver in that a user may easily incorporate his/her own string functions into the solver by simply providing code for the pre-image computation without worrying about other parts of the solver. Despite these, the semantic conditions are unfortunately too general to provide a fast and complete decision procedure. We provide strong theoretical evidence for this in the form of complexity results.To rectify this problem, we propose two solutions. Our main solution is to allow only partial string functions (i.e., prohibit nondeterminism) in condition (2). This restriction is satisfied in many cases in practice, and yields decision procedures that are effective in both theory and practice. Whenever nondeterministic functions are still needed (e.g. the string function split), our second solution is to provide a syntactic fragment that provides a support of nondeterministic functions, and operations like one-way transducers, replace-all (with constant replacement string), the string-reverse function, concatenation, and regular-expression matching. We show that this fragment can be reduced to an existing solver SLOTH that exploits fast model checking algorithms like IC3.
We provide an efficient implementation of our decision procedure (assuming our first solution above, i.e., deterministic partial string functions) in a new string solver OSTRICH. Our implementation provides in-built support for concatenation, reverse, transducers, and replace-all and provides a framework for extensibility to support further string functions. We demonstrate the efficacy of our new solver against other competitive solvers.
|Decision Procedures for Path Feasibility of String-Manipulating Programs with Complex Operations (popl19-ostrich-submitted.pdf)||802KiB|