Cong Tian

A decision procedure for propositional projection temporal logic with infinite models

This paper investigates the satisfiability of Propositional Projection Temporal Logic (PPTL) with infinite models. A decision procedure for PPTL formulas is given. To this end, Normal Form (NF) and Labeled Normal Form Graph (LNFG) for PPTL formulas are defined, and algorithms for transforming a formula to its normal form and constructing the LNFG for the given formula are presented. Further, the finiteness of LNFGs is proved in details. Moreover, the decision procedure is extended to check the satisfiability of the formulas of Propositional Interval Temporal Logic. In addition, examples are also given to illustrate how the decision procedure works.

A Unified Model Checking Approach with Projection Temporal Logic

This paper presents a unified model checking approach with Projection Temporal Logic (PTL) based on Normal Form Graphs (NFGs). To this end, a Modeling, Simulation and Verification Language (MSVL) is defined based on PTL. Further, normal forms and NFGs for MSVL programs and Propositional PTL (PPTL) formulas are defined. The finiteness for NFGs of MSVL programs is proved in details. Moreover, by modeling a system with an MSVL program p, and specifying the desirable property of the system with a PPTL formula i¾?, whether or not the system satisfies the property (whether or not pi¾?i¾?is valid) can equivalently be checked by evaluating whether or not ¬(pi¾?i¾?) i¾? pi¾? ¬i¾?is unsatisfiable. Finally, the satisfiability of a formula in the form of pi¾? ¬i¾?is checked by constructing the NFG of pi¾? ¬i¾?, and then inspecting whether or not there exist paths in the NFG.

Model checking propositional projection temporal logic based on SPIN

This paper investigates a model checking algorithm for Propositional Projection Temporal Logic (PPTL) with finite models. To this end, a PPTL formula is transformed to a Normal Form Graph (NFG), and then a Nondeterministic Finite Automaton (NFA). The NFA precisely characterizes the finite models satisfying the corresponding formula and can be equivalently represented as a Deterministic Finite Automaton (DFA). When the system to be verified can be modeled as a DFA As, and the property of the system can be specified by a PPTL formula P, then ¬P can be transformed to a DFA Ap. Thus, whether the system satisfies the property or not can be checked by computing the product automaton of As and Ap, and then checking whether or not the product automaton accepts the empty word. Further, this method can be implemented by means of the verification system SPIN.

Complexity of propositional projection temporal logic with star

This paper investigates the complexity of Propositional Projection Temporal Logic with Star (PPTL*). To this end, Propositional Projection Temporal Logic (PPTL) is first extended to include projection star. Then, by reducing the emptiness problem of star-free expressions to the problem of the satisfiability of PPTL* formulas, the lower bound of the complexity for the satisfiability of PPTL* formulas is proved to be non-elementary. Then, to prove the decidability of PPTL*, the normal form, normal form graph (NFG) and labelled normal form graph (LNFG) for PPTL* are defined. Also, algorithms for transforming a formula to its normal form and LNFG are presented. Finally, a decision algorithm for checking the satisfiability of PPTL* formulas is formalised using LNFGs.

Expressiveness of propositional projection temporal logic with star

This paper investigates the expressiveness of Propositional Projection Temporal Logic with Star (PPTL*). To this end, Buchi automata and @w-regular expressions are first extended as Stutter Buchi Automata (SBA) and Extended Regular Expressions (ERE) to include both finite and infinite strings. Further, by equivalent transformations among PPTL* formulas, SBAs and EREs, PPTL* is proved to represent exactly the full regular language. Moreover, some fragments of PPTL* are characterized, and finally, PPTL* and its fragments are classified into five different language classes.

A practical decision procedure for Propositional Projection Temporal Logic with infinite models

This paper presents a practical decision procedure for Propositional Projection Temporal Logic with infinite models. First, a set Prop l of labels l i , 0 ≤ i ≤ n ? N 0 , is used to mark nodes of an LNFG of a formula, and a node with l i is treated as an accepting state as in an automaton. Further, the generalized Buchi accepting condition for automata is employed to identify a path (resulting a word) in an LNFG as a model of the formula. In addition, the implementation details of the decision procedure and relevant algorithms including pre-processing, LNFG, circle finding algorithms are presented; as a matter of fact, all algorithms are implemented by C++ programs.

Propositional projection temporal logic, Büchi automata and ω-regular expressions

A rack for shipping flat glass sheets has a slanted backwall between a pair of standards and a base to support the sheets on edge sloped toward the backwall for shipping and packing stability. A front restraint having a pair of vertical posts and sheet engaging surface therebetween is mounted in the base and urged toward the backwall against the sheet by a compression tool. A rod pivotally mounted on each of the standards is detachably secured to the post of the front restraint. Lateral motion of the sheets is eliminated by end restraints mounted on the sides of the base. An adjustable dunnage member made of interlocking polystyrene pieces is used as a filler to secure less than a full load of sheets in the rack. An adjustable outrigger mounted on the base is employed as a filler for space between racks when loaded on a railcar or trailer.

A cylinder computation model for many-core parallel computing

Many-core parallel computing and programming are new challenges to formal specification and verification. This paper presents a semantic model for many-core parallel computing systems so that the systems can be modeled and verified in a manageable way. The model is called Cylinder Computation Model (CCM) which is based on projection constructs in Projection Temporal Logic (PTL) and Modeling, Simulation and Verification Language (MSVL). To this end, the syntax and semantics of CCM are presented in detail. Further, some logic laws regarding CCM are given and the normal form of CCM programs is formalized and proved. Moreover, the operational semantics of CCM and an algorithm for implementing CCM programs within MSVL are also demonstrated. Finally, an example, simple word processor, is given to show how CCM works under MSVL paradigm.

Towards more accurate content categorization of API discussions

Nowadays, software developers often discuss the usage of various APIs in online forums. Automatically assigning pre-defined semantic categorizes to API discussions in these forums could help manage the data in online forums, and assist developers to search for useful information. We refer to this process as content categorization of API discussions. To solve this problem, Hou and Mo proposed the usage of naive Bayes multinomial, which is an effective classification algorithm. In this paper, we propose a Cache-bAsed compoSitE algorithm, short formed as CASE, to automatically categorize API discussions. Considering that the content of an API discussion contains both textual description and source code, CASE has 3 components that analyze an API discussion in 3 different ways: text, code, and original. In the text component, CASE only considers the textual description; in the code component, CASE only considers the source code; in the original component, CASE considers the original content of an API discussion which might include textual description and source code. Next, for each component, since different terms (i.e., words) have different affinities to different categories, CASE caches a subset of terms which have the highest affinity scores to each category, and builds a classifier based on the cached terms. Finally, CASE combines all the 3 classifiers to achieve a better accuracy score. We evaluate the performance of CASE on 3 datasets which contain a total of 1,035 API discussions. The experiment results show that CASE achieves accuracy scores of 0.69, 0.77, and 0.96 for the 3 datasets respectively, which outperforms the state-of-the-art method proposed by Hou and Mo by 11%, 10%, and 2%, respectively.

An improved decision procedure for propositional projection temporal logic

A new decision procedure for Propositional Projection Temporal Logic (PPTL) is proposed which is an improvement to the decision procedure given in [4]. The main contribution of the paper is as follows: (1) the relationship between paths in the NFG of a formula R and its models is established and proved; (2) a new Labeled NFG (LNFG) with a set of labels (propositions) is defined; (3) given a formula R, an LNFG of R can be generated by the new decision algorithm, and all models of R can be found; (4) based on the new decision procedure, an improved model checking algorithm is presented and implemented.