Decidability Results for the Boundedness Problem
نویسندگان
چکیده
We prove decidability of the boundedness problem for monadic least fixed-point recursion based on positive monadic second-order (MSO) formulae over trees. Given an MSO-formula φ(X,x) that is positive in X, it is decidable whether the fixed-point recursion based on φ is spurious over the class of all trees in the sense that there is some uniform finite bound for the number of iterations φ takes to reach its least fixed point, uniformly across all trees. We also identify the exact complexity of this problem. The proof uses automata-theoretic techniques. This key result extends, by means of model-theoretic interpretations, to show decidability of the boundedness problem for MSO and guarded second-order logic (GSO) over the classes of structures of fixed finite tree-width. Further model-theoretic transfer arguments allow us to derive major known decidability results for boundedness for fragments of first-order logic as well as new ones.
منابع مشابه
Decidability and complexity of Petri nets with unordered data
We prove several decidability and undecidability results for ν-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of ν-PN strictly surpasses that of P/T nets. We encode ν-PN into Petri Data Nets, so that coverability, termination...
متن کاملDecision Problems for Petri Nets with Names
We prove several decidability and undecidability results for ν-PN, an extension of P/T nets with pure name creation and name management. We give a simple proof of undecidability of reachability, by reducing reachability in nets with inhibitor arcs to it. Thus, the expressive power of ν-PN strictly surpasses that of P/T nets. We prove that ν-PN are Well Structured Transition Systems. In particul...
متن کاملObject Petri Nets: Definitions, Properties, and Related Models
In this presentation the decidability issues of formalisms that allow Petri nets as tokens are studied. Especially for “elementary object-net systems” defined by Valk the decidability of the reachability and the boundedness problem is considered. It is shown that reachability becomes undecidable while boundedness remains decidable for elementary object-net systems. Furthermore it is shown that ...
متن کاملDecidability Problems of a Basic Class of Object Nets
It is shown that the boundedness problem for a certain class of basic object nets and a corresponding class of multiset rewriting systems is decidable. To achieve this result Dickson’s Lemma for a certain class of multisets, and a modified Karp Miller algorithm, is applied. This presents another class of nets with different decidability behaviour for reachability and boundedness.
متن کاملOn the Boundedness Problem for Two-Variable First-Order Logic
A positive rst-order formula is bounded if the sequence of its stages converges to the least xed point of the formula within a xed nite number of steps independent of the input structure. The boundedness problem for a fragment L of rst-order logic is the following decision problem: given a positive formula in L, is it bounded? In this paper, we investigate the boundedness problem for two-variab...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Logical Methods in Computer Science
دوره 10 شماره
صفحات -
تاریخ انتشار 2014