Unification Modulo Presburger Arithmetic and Other Decidable Theories
نویسندگان
چکیده
We present a general uni cation algorithm modulo Presburger Arithmetic for a restricted class of modularly speci ed theories where function symbols of the target theory have non arithmetic codomain sorts. Additionally, we comment on conditions guaranteeing decidability of matching and uni cation problems modulo more general theories than the arithmetic ones, which appear when automated deduction is implemented by combining conditional rewriting techniques and decision algorithms for built-in predi-
منابع مشابه
On Sets with Cardinality Constraints in Satisfiability Modulo Theories
Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier-free BAPA (QFBAPA). Deciding the satisfiability of QFBAPA formulas has been shown to be NP-complete using an eager reduction to quantifier-fr...
متن کاملApplications of Decision Algorithms for Presburger Arithmetic in Rewrite Automated Deduction
We present some slight improvements to a semi-decision algorithm for Presburger arithmetic originally developed by Shostak that increase the class of formulas eeectively decidable. Furthermore , we show how decision algorithms for Presburger arithmetic may be combined with conditional rewrite techniques for automated deduction in algebraic speciications presented by conditional equational claus...
متن کاملSets with Cardinality Constraints in Satisfiability Modulo Theories
Boolean Algebra with Presburger Arithmetic (BAPA) is a decidable logic that can express constraints on sets of elements and their cardinalities. Problems from verification of complex properties of software often contain fragments that belong to quantifier-free BAPA (QFBAPA). In contrast to many other NP-complete problems (such as quantifier-free first-order logic or linear arithmetic), the appl...
متن کاملVariant-Based Decidable Satisfiability in Initial Algebras with Predicates
Decision procedures can be either theory specific, e.g., Presburger arithmetic, or theory-generic, applying to an infinite number of user-definable theories. Variant satisfiability is a theory-generic procedure for quantifier-free satisfiability in the initial algebra of an ordersorted equational theory pΣ,EYBq under two conditions: (i) EYB has the finite variant property and B has a finitary u...
متن کاملWhat's Decidable about Availability Languages?
We study here the algorithmic analysis of systems modeled in terms of availability languages. Our first main result is a positive answer to the emptiness problem: it is decidable whether a given availability language contains a word. The key idea is an inductive construction that replaces availability languages with Parikh-equivalent regular languages. As a second contribution, we solve the int...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Revista Colombiana de Computación
دوره 2 شماره
صفحات -
تاریخ انتشار 2001