Country Snapshot North Macedonia

A brief summary of the history and current status of religion in North Macedonia

Deciding regular grammar logics with converse through first-order logic

We provide a simple translation of the satisfiability problem for regular grammar logics with converse into GF2, which is the intersection of the guarded fragment and the 2-variable fragment of first-order logic. This translation is theoretically interesting because it translates modal logics with certain frame conditions into first-order logic, without explicitly expressing the frame conditions. A consequence of the translation is that the general satisfiability problem for regular grammar logics with converse is in EXPTIME. This extends a previous result of the first author for grammar logics without converse. Using the same method, we show how some other modal logics can be naturally translated into GF2, including nominal tense logics and intuitionistic logic. In our view, the results in this paper show that the natural first-order fragment corresponding to regular grammar logics is simply GF2 without extra machinery such as fixed point-operators.Comment: 34 page

Modal Logics with Hard Diamond-free Fragments

We investigate the complexity of modal satisfiability for certain combinations of modal logics. In particular we examine four examples of multimodal logics with dependencies and demonstrate that even if we restrict our inputs to diamond-free formulas (in negation normal form), these logics still have a high complexity. This result illustrates that having D as one or more of the combined logics, as well as the interdependencies among logics can be important sources of complexity even in the absence of diamonds and even when at the same time in our formulas we allow only one propositional variable. We then further investigate and characterize the complexity of the diamond-free, 1-variable fragments of multimodal logics in a general setting.Comment: New version: improvements and corrections according to reviewers' comments. Accepted at LFCS 201

Satisfiability of CTL* with constraints

We show that satisfiability for CTL* with equality-, order-, and modulo-constraints over Z is decidable. Previously, decidability was only known for certain fragments of CTL*, e.g., the existential and positive fragments and EF.Comment: To appear at Concur 201

The Effect Of Human Resources Development And Motivation On Increasing Performance Of Widyaiswara At The Guarantee Development Center Quality Of Vocational Education Field Building And Electricity (BBPPMPV BBL) Medan

There are many factors that affect the performance of widyaiswara (Civil Servant (PNS) who is appointed as a functional official by an authorized official with the duties, responsibilities, authority to educate, teach, and/or train Civil Servants (PNS) in government education and training institutions) including human resource development and motivation. The purpose of this study is to determine the effect of human resource development and motivation partially on the performance of widyaiswara at BBPMPPV BBL Medan. The population of this study found 50 widyaiswara BBPMPPV BBL Medan. Data collection techniques in this study are questionnaires, interviews and documentation studies. While the data analysis techniques used are classical assumption test, multiple regression, T- test, F- test and coefficient of determination. The results showed that the HR development variable had a significant effect on the performance of widyaiswara at BBPMPPV BBL Medan. The better the development of human resources, the performance of the widyaiswara will also be higher. The motivation variable has a significant effect on the performance of widyaiswara at BBPMPPV BBL Medan. The better the motivation, the higher the widyaiswara's performance. There is a significant influence of the variables of human resource development and motivation simultaneously on the performance of widyaiswara at BBPMPPV BBL Medan. The coefficient of determination with a value of 85.50% widyaiswara variation can be explained by the variables of human resource development and motivation simultaneously, while the remaining 14.50% is explained by other factors, such as variables of work ability and work discipline

On Temporal and Separation Logics

International audienceThere exist many success stories about the introduction of logics designed for the formal verification of computer systems. Obviously, the introduction of temporal logics to computer science has been a major step in the development of model-checking techniques. More recently, separation logics extend Hoare logic for reasoning about programs with dynamic data structures, leading to many contributions on theory, tools and applications. In this talk, we illustrate how several features of separation logics, for instance the key concept of separation, are related to similar notions in temporal logics. We provide formal correspondences (when possible) and present an overview of related works from the literature. This is also the opportunity to present bridges between well-known temporal logics and more recent separation logics

Reasoning about reversal-bounded counter machines

International audienceIn this paper, we present a short survey on reversal-bounded counter machines. It focuses on the main techniques for model-checking such counter machines with specifications expressed with formulae from some linear-time temporal logic. All the decision procedures are designed by translation into Presburger arithmetic. We provide a proof that is alternative to Ibarra's original one for showing that reachability sets are effectively definable in Presburger arithmetic. Extensions to repeated control state reachability and to additional temporal properties are discussed in the paper. The article is written to the honor of Professor Ewa Orłowska and focuses on several topics that are developped in her works

Why Propositional Quantification Makes Modal Logics on Trees Robustly Hard?

International audienceAdding propositional quantification to the modal logics K, T or S4 is known to lead to undecid-ability but CTL with propositional quantification under the tree semantics (QCTL t) admits a non-elementary Tower-complete satisfiability problem. We investigate the complexity of strict fragments of QCTL t as well as of the modal logic K with propositional quantification under the tree semantics. More specifically, we show that QCTL t restricted to the temporal operator EX is already Tower-hard, which is unexpected as EX can only enforce local properties. When QCTL t restricted to EX is interpreted on N-bounded trees for some N ≥ 2, we prove that the satisfiability problem is AExp pol-complete; AExp pol-hardness is established by reduction from a recently introduced tiling problem, instrumental for studying the model-checking problem for interval temporal logics. As consequences of our proof method, we prove Tower-hardness of QCTL t restricted to EF or to EXEF and of the well-known modal logics K, KD, GL, S4, K4 and D4, with propositional quantification under a semantics based on classes of trees