اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدDecomposition of Decidable First-Order Logics over Integers and Reals
180
0
0.0
(
0
)
تأليف
Florent Bouchy
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We tackle the issue of representing infinite sets of real- valued vectors. This paper introduces an operator for combining integer and real sets. Using this operator, we decompose three well-known logics extending Presburger with reals. Our decomposition splits a logic into two parts : one integer, and one decimal (i.e. on the interval [0,1]). We also give a basis for an implementation of our representation.
قيم البحث
اقرأ أيضاً
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We provide n
ew temporal logics for finite and infinite nested words, which are natural extensions of LTL, and prove that these logics are first-order expressively-complete. One of them is based on adding a within modality, evaluating a formula on a subword, to a logic CaRet previously studied in the context of verifying properties of recursive state machines (RSMs). The other logic, NWTL, is based on the notion of a summary path that uses both the linear and nesting structures. For NWTL we show that satisfiability is EXPTIME-complete, and that model-checking can be done in time polynomial in the size of the RSM model and exponential in the size of the NWTL formula (and is also EXPTIME-complete). Finally, we prove that first-order logic over nested words has the three-variable property, and we present a temporal logic for nested words which is complete for the two-variable fragment of first-order.
We show that the techniques for resource control that have been developed in the so-called light logics can be fruitfully applied also to process algebras. In particular, we present a restriction of Higher-Order pi-calculus inspired by Soft Linear Lo
gic. We prove that any soft process terminates in polynomial time. We argue that the class of soft processes may be naturally enlarged so that interesting processes are expressible, still maintaining the polynomial bound on executions.
This paper examines the complexity of hybrid logics over transitive frames, transitive trees, and linear frames. We show that satisfiability over transitive frames for the hybrid language extended with the downarrow operator is NEXPTIME-complete. Thi
s is in contrast to undecidability of satisfiability over arbitrary frames for this language (Areces, Blackburn, Marx 1999). It is also shown that adding the @ operator or the past modality leads to undecidability over transitive frames. This is again in contrast to the case of transitive trees and linear frames, where we show these languages to be nonelementarily decidable. Moreover, we establish 2EXPTIME and EXPTIME upper bounds for satisfiability over transitive frames and transitive trees, respectively, for the hybrid Until/Since language. An EXPTIME lower bound is shown to hold for the modal Until language over both frame classes.
We study complexity of the model-checking problems for LTL with registers (also known as freeze LTL) and for first-order logic with data equality tests over one-counter automata. We consider several classes of one-counter automata (mainly determinist
ic vs. nondeterministic) and several logical fragments (restriction on the number of registers or variables and on the use of propositional variables for control locations). The logics have the ability to store a counter value and to test it later against the current counter value. We show that model checking over deterministic one-counter automata is PSPACE-complete with infinite and finite accepting runs. By constrast, we prove that model checking freeze LTL in which the until operator is restricted to the eventually operator over nondeterministic one-counter automata is undecidable even if only one register is used and with no propositional variable. As a corollary of our proof, this also holds for first-order logic with data equality tests restricted to two variables. This makes a difference with the facts that several verification problems for one-counter automata are known to be decidable with relatively low complexity, and that finitary satisfiability for the two logics are decidable. Our results pave the way for model-checking memoryful (linear-time) logics over other classes of operational models, such as reversal-bounded counter machines.
This volume contains the proceedings of the First Workshop on Logics and Model-checking for self-* systems (MOD* 2014). The worshop took place in Bertinoro, Italy, on 12th of September 2014, and was a satellite event of iFM 2014 (the 11th Internation
al Conference on Integrated Formal Methods). The workshop focuses on demonstrating the applicability of Formal Methods on modern complex systems with a high degree of self-adaptivity and reconfigurability, by bringing together researchers and practitioners with the goal of pushing forward the state of the art on logics and model checking.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
