Design and Implementation of Bounded-Length Sequence Variables

Abstract

We present the design and implementation of bounded-length sequence (BLS) variables for a CP solver. The domain of a BLS variable is represented as the combination of a set of candidate lengths and a sequence of sets of candidate characters. We show how this representation, together with requirements imposed by propagators, affects the implementation of BLS variables for a copying CP solver, most importantly the closely related decisions of data structure, domain restriction operations, and propagation events. The resulting implementation outperforms traditional bounded-length string representations for CP solvers, which use a fixed-length array of candidate characters and a padding symbol.

Dashed Strings and the Replace(-all) Constraint

“…Gecode+S [28] instead defines dedicated propagators for string constraints. The unfolding approach adds flexibility but may sacrifice high-level relationships between strings, cannot deal with unbounded-length strings and may be very inefficient when the length bound is large-even if the generated solutions have short length.…”

Constraint Programming for Dynamic Symbolic Execution of JavaScript

“…Different approaches to string constraint solving have been proposed, based on: automata [25,31,47], word equations [13,32], unfolding (using either bitvector solvers [27,42] or CP [43]), and dashed strings [7,8]. In particular, dashed strings are a recent CP approach that can be seen as "lazy" unfolding.…”

“…MiniZinc was equipped with string variables and constraints by Amadini et al [3]. A MiniZinc model with strings can be solved "directly" by CP solvers natively supporting string variables (Gecode+S [43] and G-Strings [7]) or "indirectly" via the static unfolding into integer variables. Clearly, direct resolution is generally more efficient-especially as λ grows.…”

Propagating Regular Membership with Dashed Strings

“…For unfolding-based string constraint solvers like [18], these regular propagators may be used directly. Given automaton Q, Σ, q 0 , δ, F , if is the null symbol used to pad strings of length smaller than λ, it is enough to introduce a fresh state q , such that δ(q , c) = q , for each c ∈ Σ, q ∈ F ∪ {q }.…”

“…String constraint solving is an emerging topic that bases its motivation in fields like web security and software analysis and verification. Suitable solvers have been introduced over the last years for solving combinatorial problems involving string variables and constraints [1,9,12,14,[18][19][20][21].…”