Related papers: Decidable Logics Combining Word Equations, Regular…
In this paper, we consider the satisfiability problem for string logic with equations, regular membership and Presburger constraints over length functions. The difficulty comes from multiple occurrences of string variables making…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings, which have received a lot of attention in recent years. A word equation relates two words over string variables and constants. Its…
Word equations are a crucial element in the theoretical foundation of constraint solving over strings. A word equation relates two words over string variables and constants. Its solution amounts to a function mapping variables to constant…
We prove several decidability and undecidability results for the satisfiability and validity problems for languages that can express solutions to word equations with length constraints. The atomic formulas over this language are equality…
We consider the extension of two variable logic with quantifiers that state that the number of elements where a formula holds should belong to a given ultimately periodic set. We show that both satisfiability and finite satisfiability of…
We consider the one-variable fragment of first-order logic extended with Presburger constraints. The logic is designed in such a way that it subsumes the previously-known fragments extended with counting, modulo counting or cardinality…
We address the satisfiability problem for string constraints that combine relational constraints represented by transducers, word equations, and string length constraints. This problem is undecidable in general. Therefore, we propose a new…
Satisfiability of word equations is an important problem in the intersection of formal languages and algebra: Given two sequences consisting of letters and variables we are to decide whether there is a substitution for the variables that…
We present new results on finite satisfiability of logics with counting and arithmetic. One result is a tight bound on the complexity of satisfiability of logics with so-called local Presburger quantifiers, which sum over neighbors of a…
We study the fundamental issue of decidability of satisfiability over string logics with concatenations and finite-state transducers as atomic operations. Although restricting to one type of operations yields decidability, little is known…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
We investigate the properties of formal languages expressible in terms of formulas over quantifier-free theories of word equations, arithmetic over length constraints, and language membership predicates for the classes of regular, visibly…
Widespread use of string solvers in formal analysis of string-heavy programs has led to a growing demand for more efficient and reliable techniques which can be applied in this context, especially for real-world cases. Designing an…
The satisfiability problem of hybrid logics with the downarrow binder is known to be undecidable. This initiated a research program on decidable and tractable fragments. In this paper, we investigate the effect of restricting the…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
The first-order theory of addition over the natural numbers, known as Presburger arithmetic, is decidable in double exponential time. Adding an uninterpreted unary predicate to the language leads to an undecidable theory. We sharpen the…
In this paper, we investigate the expressive power and the algorithmic properties of weighted expressions, which define functions from finite words to integers. First, we consider a slight extension of an expression formalism, introduced by…
We present Woorpje, a string solver for bounded word equations (i.e., equations where the length of each variable is upper bounded by a given integer). Our algorithm works by reformulating the satisfiability of bounded word equations as a…
When eating spaghetti, one should have the sauce and noodles mixed instead of eating them separately. We argue that also in string solving, word equations and regular constraints are better mixed together than approached separately as in…
During the last decades, a lot of effort was put into identifying decidable fragments of first-order logic. Such efforts gave birth, among the others, to the two-variable fragment and the guarded fragment, depending on the type of…