Some properties of CTL
نویسنده
چکیده
1 CTL formulae We formalize basic concepts of Computational Tree Logic (CTL) [2, 1] within the simply-typed set theory of HOL. By using the common technique of “shallow embedding”, a CTL formula is identified with the corresponding set of states where it holds. Consequently, CTL operations such as negation, conjunction, disjunction simply become complement, intersection, union of sets. We only require a separate operation for implication, as point-wise inclusion is usually not encountered in plain set-theory. lemmas [intro!] = Int-greatest Un-upper2 Un-upper1 Int-lower1 Int-lower2 types ′a ctl = ′a set constdefs imp :: ′a ctl ⇒ ′a ctl ⇒ ′a ctl (infixr → 75 ) p → q ≡ − p ∪ q lemma [intro!]: p ∩ p → q ⊆ q by (unfold imp-def ) auto lemma [intro!]: p ⊆ (q → p) by (unfold imp-def ) rule
منابع مشابه
Computation Tree Logic Model Checking Based on Possibility Measures
In order to deal with the systematic verification with uncertain infromation in possibility theory, Li and Li [19] introduced model checking of linear-time properties in which the uncertainty is modeled by possibility measures. Xue, Lei and Li [26] defined computation tree logic (CTL) based on possibility measures, which is called possibilistic CTL (PoCTL). This paper is a continuation of the a...
متن کاملMeet- and join-closure of CTL operators
Results from lattice theory have successfully been applied by several researchers, e.g. [1, 7, 9, 10], to reduce the complexity of verification of distributed computations. The set of all reachable states of a distributed computation forms a lattice under a certain partial order relation. A property is said to exhibit meet-closure if the set of reachable states satisfying it is closed under the...
متن کاملCTL Property Language in Formal Verification of Systems A System Approach
We use symbolic model checking to verify a VHDL design. This paper mainly focuses on Computational Tree Logic (CTL) for model checking problem. We have explained these two terms “CTL” and “model checking” for providing a clear idea about these two. Most importantly we have explored the ways of uses of CTL formulae in the case of model checking. The importance of the model checking, the ways of ...
متن کاملUsing Natural Language Documentation in the Formal Verification of Hardware Designs
In the modern ASIC design cycle, correctness properties for functional verification are usually created by an engineer whose task is to read the system documentation and manually generate a set of formal statements in the chosen verification language. This process is typical of the reason why up to 60% of engineering effort is spent on verification and test activities. We present a formal attri...
متن کاملA Probabilistic Temporal Logic with Frequency Operators and Its Model Checking
Probabilistic Computation Tree Logic (PCTL) and Continuous Stochastic Logic (CSL) are often used to describe specifications of probabilistic properties for discrete time and continuous time, respectively. In PCTL and CSL, the possibility of executions satisfying some temporal properties can be quantitatively represented by the probabilistic extension of the path quantifiers in their basic Compu...
متن کاملReasoning about Choice
We present a logic for reasoning about choice. Choice CTL (C-CTL) extends the well-known branching-time temporal logic CTL with choice modalities, “3” and “2”. An example C-CTL formula is 3AFhappy , asserting that there exists a choice that will lead to happiness. C-CTL is related to both STIT logics and temporal cooperation logics such as ATL, but has a much simpler and (we argue) more intuiti...
متن کامل