اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدReasoning About Bounds in Weighted Transition Systems
131
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates states that exhibit transitions to bisimulation classes with the weights within the same boundaries. We propose a customized modal logic that expresses these numeric boundaries for transition weights by means of particular modalities. We prove that our logic is invariant under the proposed notion of bisimulation. We show that the logic enjoys the finite model property and we identify a complete axiomatization for the logic. Last but not least, we use a tableau method to show that the satisfiability problem for the logic is decidable.
قيم البحث
اقرأ أيضاً
This paper presents a Hoare-style calculus for formal reasoning about reconfiguration programs of distributed systems. Such programs delete or create interactions or components while the system components change state according to their local behavio
ur. Our proof calculus uses a configuration logic that supports local reasoning and that relies on inductive predicates to describe distributed systems with an unbounded number of components. The validity of reconfiguration programs relies on havoc invariants, assertions about the ongoing interactions in the system. We present a proof system for such invariants in an assume/rely-guarantee style. We illustrate the feasibility of our approach by proving the correctness of self-adjustable tree architectures and provide tight complexity bounds for entailment checking in the configuration logic.
We introduce a logical framework for the specification and verification of component-based systems, in which finitely many component instances are active, but the bound on their number is not known. Besides specifying and verifying parametric systems
, we consider the aspect of dynamic reconfiguration, in which components can migrate at runtime on a physical map, whose shape and size may change. We describe such parametric and reconfigurable architectures using resource logics, close in spirit to Separation Logic, used to reason about dynamic pointer structures. These logics support the principle of local reasoning, which is the key for writing modular specifications and building scalable verification algorithms, that deal with large industrial-size systems.
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected that recursi
on will become one of the fundamental paradigms of quantum programming. Several program logics have been developed for verification of quantum while-programs. However, there are as yet no general methods for reasoning about (mutual) recursive procedures and ancilla quantum data structure in quantum computing (with measurement). We fill the gap in this paper by proposing a parameterized quantum assertion logic and, based on which, designing a quantum Hoare logic for verifying parameterized recursive quantum programs with ancilla data and probabilistic control. The quantum Hoare logic can be used to prove partial, total, and even probabilistic correctness (by reducing to total correctness) of those quantum programs. In particular, two counterexamples for illustrating incompleteness of non-parameterized assertions in verifying recursive procedures, and, one counterexample for showing the failure of reasoning with exact probabilities based on partial correctness, are constructed. The effectiveness of our logic is shown by three main examples -- recursive quantum Markov chain (with probabilistic control), fixed-point Grovers search, and recursive quantum Fourier sampling.
Let S be a commutative semiring. M. Droste and P. Gastin have introduced in 2005 weighted monadic second order logic WMSOL with weights in S. They use a syntactic fragment RMSOL of WMSOL to characterize word functions (power series) recognizable by w
eighted automata, where the semantics of quantifiers is used both as arithmetical operations and, in the boolean case, as quantification. Already in 2001, B. Courcelle, J.Makowsky and U. Rotics have introduced a formalism for graph parameters definable in Monadic Second order Logic, here called MSOLEVAL with values in a ring R. Their framework can be easily adapted to semirings S. This formalism clearly separates the logical part from the arithmetical part and also applies to word functions. In this paper we give two proofs that RMSOL and MSOLEVAL with values in S have the same expressive power over words. One proof shows directly that MSOLEVAL captures the functions recognizable by weighted automata. The other proof shows how to translate the formalisms from one into the other.
In functional programming, datatypes a la carte provide a convenient modular representation of recursive datatypes, based on their initial algebra semantics. Unfortunately it is highly challenging to implement this technique in proof assistants that
are based on type theory, like Coq. The reason is that it involves type definitions, such as those of type-level fixpoint operators, that are not strictly positive. The known work-around of impredicative encodings is problematic, insofar as it impedes conventional inductive reasoning. Weak induction principles can be used instead, but they considerably complicate proofs. This paper proposes a novel and simpler technique to reason inductively about impredicative encodings, based on Mendler-style induction. This technique involves dispensing with dependent induction, ensuring that datatypes can be lifted to predicates and relying on relational formulations. A case study on proving subject reduction for structural operational semantics illustrates that the approach enables modular proofs, and that these proofs are essentially similar to conventional ones.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
