Extended Temporal Logic Revisited

Abstract

Abstract.A key issue in the design of a model-checking tool is the choice of the formal language with which properties are specified. It is now recognized that a good language should extend linear temporal logic with the ability to specify all -regular properties. Also, designers, who are familiar with finite-state machines, prefer extensions based on automata than these based on fixed points or propositional quantification. Early extensions of linear temporal logic with automata use nondeterministic Büchi automata. Their drawback has been inability to refer to the past and the asymmetrical structure of nondeterministic automata. In this work we study an extension of linear temporal logic, called ETL © , that uses two-way alternating automata as temporal connectives. Two-way automata can traverse the input word back and forth and they are exponentially more succinct than one-way automata. Alternating automata combine existential and universal branching and they are exponentially more succinct than nondeterministic automata. The rich structure of two-way alternating automata makes ETL © a very powerful and convenient logic. We show that ETL © formulas can be translated to nondeterministic Büchi automata with an exponential blow up. It follows that the satisfiability and model-checking problems for ETL © are PSPACEcomplete, as are the ones for LTL and its earlier extensions with automata. So, in spite of the succinctness of two-way and alternating automata, the advantages of ETL © are obtained without a major increase in space complexity. The recent acceptance of alternating automata by the industry and the development of symbolic procedures for handling them make us optimistic about the practicality of ETL © .

Efficient Regular Linear Temporal Logic Using Dualization and Stratification

“…The main result is the specialization of Street rankings to stratified automata to obtain a more efficient ranking translation. Unlike [11] our construction preserves the alphabet between the alternating automaton an the NBW. We are currently investigating alternative algorithms for model-checking RLTL specifications based on bounded model checking [17], antichains [18] and IC3 [19].…”

“…Here, we use again the particular stratified structure of the ASW{1} automata obtained from RLTL expressions. Each stratum in the generated ASW{1} is either Büchi (only colors 1 and 2) or coBüchi (colors 0 and 1), making these automata equivalent to hesitant automata AHW (see [11]). We introduce a notion of stratified ranking and show that for all RLTL operators (except one), the ranking of each state can be statically predetermined.…”

Monodic temporal logic with quantified propositional variables

“…The resulting logic QPTL is decidable, but with non-elementary complexity. Other ways of achieving the expressive power of QPTL include the use of right-linear grammar operators as in ETL [21], the linear µ-calculus [2], and the use of various kinds of automata as temporal connectives [20], [15]. These alternative methods have often been preferred to propositional quantification because of elementary decision problems, and have given rise to extensions in a wide range of logics from Extended CTL* to Automata Logic [5].…”

Temporal logic with forgettable past

“…Regarding lower bounds, the non-existence of succinct translations has been conjectured (e.g. [13]) but not yet proved.…”

“…[8,15,14,16]. Automata-theoretic methods for temporal-logics were pioneered by Vardi and Wolper, and they were adapted for LTL + Past and mu-calculus + Past in [17,23,12,13] (these logics have PSPACE-complete verification problems). N can be encoded in richer formalisms, e.g.…”