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On regular temporal logics with past
- In Proceedings of the 36th International Colloquium on Automata, Languages, and Programming (ICALP), volume 5556 of Lect. Notes Comput. Sci
"... Abstract. The IEEE standardized Property Specification Language, PSL for short, extends the well-known linear-time temporal logic LTL with so-called semi-extended regular expressions. PSL and the closely related SystemVerilog Assertions, SVA for short, are increasingly used in many phases of the har ..."
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Abstract. The IEEE standardized Property Specification Language, PSL for short, extends the well-known linear-time temporal logic LTL with so-called semi-extended regular expressions. PSL and the closely related SystemVerilog Assertions, SVA for short, are increasingly used in many phases of the hardware design cycle, from specification to verification. In this paper, we extend the common core of these specification lan-guages with past operators. We name this extension RTL. Although all ω-regular properties are expressible in PSL, SVA, and RTL, past opera-tors often allow one to specify properties more naturally and concisely. In fact, we show that RTL is exponentially more succinct than the cores of PSL and SVA. Furthermore, we present a translation of RTL into language-equivalent nondeterministic Büchi automata, which is based on novel constructions for 2-way alternating automata. Our translation has almost the same worst-case complexity in terms of the size of the resulting nondeterministic Büchi automata as the existing translations for PSL and SVA. Consequently, the satisfiability and the model-checking problem for RTL fall into the same complexity classes as the corresponding problems for PSL and SVA. From the translation it also follows that the blowup of translating RTL formulas into initially equivalent PSL/SVA formulas is at most triply exponential. 1
Regular Linear Temporal Logic with Past
"... Abstract. This paper upgrades Regular Linear Temporal Logic (RLTL) with past operators and complementation. RLTL is a temporal logic that extends the expressive power of linear temporal logic (LTL) to all ω-regular languages. The syntax of RLTL consists of an algebraic signature from which expressio ..."
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Abstract. This paper upgrades Regular Linear Temporal Logic (RLTL) with past operators and complementation. RLTL is a temporal logic that extends the expressive power of linear temporal logic (LTL) to all ω-regular languages. The syntax of RLTL consists of an algebraic signature from which expressions are built. In particular, RLTL does not need or expose fix-point binders (like linear time μ-calculus), or automata to build and instantiate operators (like ETL∗). Past operators are easily introduced in RLTL via a single previous-step operator for basic state formulas. The satisfiability and model checking problems for RLTL are PSPACE-complete, which is optimal for extensions of LTL. This result is shown using a novel linear size translation of RLTL expressions into 2-way alternating parity automata on words. Unlike previous automata-theoretic approaches to LTL, this construction is compositional (bottom-up). As alternating parity automata can easily be complemented, the treatment of negation is simple and does not require an upfront transformation of formulas into any normal form. 1
Augmenting a Regular Expression-Based Temporal Logic with Local Variables
"... Abstract—The semantics of temporal logic is usually defined with respect to a word representing a computation path over a set of atomic propositions. A temporal logic formula does not control the behavior of the atomic propositions, it merely observes their behavior. Local variables are a twist on t ..."
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Abstract—The semantics of temporal logic is usually defined with respect to a word representing a computation path over a set of atomic propositions. A temporal logic formula does not control the behavior of the atomic propositions, it merely observes their behavior. Local variables are a twist on this approach, in which the user can declare variables local to the formula and control their behavior from within the formula itself. Local variables were introduced in 2002, and a formal semantics was given to them in the context of SVA, the assertion language of SystemVerilog, in 2004. That semantics suffers from several drawbacks. In particular, it breaks distributivity of the operators corresponding to intersection and union. In this paper we present a formal semantics for local variables that solves that problem and others, and compare it to the previous solution. I.
Expressive Completeness of Separation Logic With Two Variables and
"... Separation logic is used as an assertion language for Hoare-style proof systems about programs with point-ers, and there is an ongoing quest for understanding its complexity and expressive power. Herein, we show that first-order separation logic with one record field restricted to two variables and ..."
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Separation logic is used as an assertion language for Hoare-style proof systems about programs with point-ers, and there is an ongoing quest for understanding its complexity and expressive power. Herein, we show that first-order separation logic with one record field restricted to two variables and the separating impli-cation (no separating conjunction) is as expressive as weak second-order logic, substantially sharpening a previous result. Capturing weak second-order logic with such a restricted form of separation logic requires substantial updates to known proof techniques. We develop these, and as a by-product identify the smallest fragment of separation logic known to be undecidable: first-order separation logic with one record field, two variables, and no separating conjunction. Because we forbid ourselves the use of many syntactic resources, this underscores even further the power of separating implication on concrete heaps.
Regular Linear-time Temporal Logic
"... Abstract—This extended abstract presents the gist of regular linear-time temporal logic (RLTL), a logic that generalizes linear-time temporal logic (LTL) with the ability to use regular expressions arbitrarily as sub-expressions. Unlike LTL, RLTL can define all ω-regular languages and unlike previou ..."
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Abstract—This extended abstract presents the gist of regular linear-time temporal logic (RLTL), a logic that generalizes linear-time temporal logic (LTL) with the ability to use regular expressions arbitrarily as sub-expressions. Unlike LTL, RLTL can define all ω-regular languages and unlike previous approaches, RLTL is defined with an algebraic signature, does not depend on fix-points in its syntax, and provides past operators via a single previous-step operator for basic state formulas. The satisfiability and model checking problems for RLTL are PSPACE-complete, which is optimal for extensions of LTL. Keywords-temporal logic; LTL; regular expressions; I.
