Extending Temporal Logics with Data Variable Quantifications

Although data values are available in almost every computer system, reasoning about them is a challenging task due to the huge data size or even infinite data domains. Temporal logics are the well-known specification formalisms for reactive and concurrent systems. Various extensions of temporal logics have been proposed to reason about data values, mostly in the last decade. Among them, one natural idea is to extend temporal logics with variable quantifications ranging over an infinite data domain. In this paper, we focus on the variable extensions of two widely used temporal logics, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). Grumberg, Kupferman and Sheinvald recently investigated the extension of LTL with variable quantifications. They defined the extension as formulas in the prenex normal form, that is, all the variable quantifications precede the LTL formulas. Our goal in this paper is to do a relatively complete investigation on this topic. For this purpose, we define the extensions of LTL and CTL by allowing arbitrary nestings of variable quantifications, Boolean and temporal operators (the resulting logics are called respectively variable-LTL, in brief VLTL, and variable-CTL, in brief VCTL), and identify the decidability frontiers of both the satisfiability and model checking problem. In particular, we obtain the following results: 1) Existential variable quantifiers or one single universal quantifier in the beginning already entails undecidability for the satisfiability problem of both VLTL and VCTL, 2) If only existential path quantifiers are used in VCTL, then the satisfiability problem is decidable, no matter which variable quantifiers are available. 3) For VLTL formulas with one single universal variable quantifier in the beginning, if the occurrences of the non-parameterized atomic propositions are guarded by the positive occurrences of the quantified variable, then its satisfiability problem becomes decidable. Based on these results of the satisfiability problem, we deduce the (un)decidability results of the model checking problem

On the satisfiability of indexed linear temporal logics

Indexed Linear Temporal Logics (ILTL) are an extension of standard Linear Temporal Logics (LTL) with quantifications over index variables which range over a set of process identifiers. ILTL has been widely used in specifying and verifying properties of parameterised systems, e.g., in parameterised model checking of concurrent processes. However there is still a lack of theoretical investigations on properties of ILTL, compared to the well-studied LTL. In this paper, we start to narrow this gap, focusing on the satisfiability problem, i.e., to decide whether a model exists for a given formula. This problem is in general undecidable. Various fragments of ILTL have been considered in the literature typically in parameterised model checking, e.g., ILTL formulae in prenex normal form, or containing only non-nested quantifiers, or admitting limited temporal operators. We carry out a thorough study on the decidability and complexity of the satisfiability problem for these fragments. Namely, for each fragment, we either show that it is undecidable, or otherwise provide tight complexity bounds

Global model checking on pushdown multi-agent systems

Pushdown multi-agent systems, modeled by pushdown game structures (PGSs), are an important paradigm of infinite-state multi-agent systems. Alternating-time temporal logics are well-known specification formalisms for multi-agent systems, where the selective path quantifier is introduced to reason about strategies of agents. In this paper, we investigate model checking algorithms for variants of alternating-time temporal logics over PGSs, initiated by Murano and Perelli at IJCAI'15. We first give a triply exponential-time model checking algorithm for ATL* over PGSs. The algorithm is based on the saturation method, and is the first global model checking algorithm with a matching lower bound. Next, we study the model checking problem for the alternating-time mu-calculus. We propose an exponential-time global model checking algorithm which extends similar algorithms for pushdown systems and modal mu-calculus. The algorithm admits a matching lower bound, which holds even for the alternation-free fragment and ATL

Tractability of Separation Logic with Inductive Definitions: Beyond Lists

In 2011, Cook et al. showed that the satisfiability and entailment can be checked in polynomial time for a fragment of separation logic that allows for reasoning about programs with pointers and linked lists. In this paper, we investigate whether the tractability results can be extended to more expressive fragments of separation logic that allow defining data structures beyond linked lists. To this end, we introduce separation logic with a simply-nonlinear compositional inductive predicate where source, destination, and static parameters are identified explicitly (SLID[snc]). We show that if the inductive predicate has more than one source (destination) parameter, the satisfiability problem for SLID[snc] becomes intractable in general. This is exemplified by an inductive predicate for doubly linked list segments. By contrast, if the inductive predicate has only one source (destination) parameter, the satisfiability and entailment problems for SLID[snc] are tractable. In particular, the tractability results hold for inductive predicates that define list segments with tail pointers and trees with one hole

Functional evaluation of Asp76, 84, 102 and 150 in human arsenic(III) methyltransferase (hAS3MT) interacting with S-adenosylmethionine

AbstractWe prepared eight mutants (D76P, D76N, D84P, D84N, D102P, D102N, D150P and D150N) to investigate the functions of residues Asp76, 84, 102 and 150 in human arsenic(III) methyltransferase (hAS3MT) interacting with the S-adenosylmethionine (SAM)-binding. The affinity of all the mutants for SAM were weakened. All the mutants except for D150N completely lost their methylation activities. Residues Asp76, 84, 102 and 150 greatly influenced hAS3MT catalytic activity via affecting SAM-binding or methyl transfer. Asp76 and 84 were located in the SAM-binding pocket, and Asp102 significantly affected SAM-binding via forming hydrogen bonds with SAM