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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 wellknown lineartime temporal logic LTL with socalled semiextended 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 wellknown lineartime temporal logic LTL with socalled semiextended 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 languages with past operators. We name this extension RTL. Although all ωregular properties are expressible in PSL, SVA, and RTL, past operators 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 languageequivalent nondeterministic Büchi automata, which is based on novel constructions for 2way alternating automata. Our translation has almost the same worstcase 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 modelchecking 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 ωregular 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 ωregular languages. The syntax of RLTL consists of an algebraic signature from which expressions are built. In particular, RLTL does not need or expose fixpoint binders (like linear time μcalculus), or automata to build and instantiate operators (like ETL∗). Past operators are easily introduced in RLTL via a single previousstep operator for basic state formulas. The satisfiability and model checking problems for RLTL are PSPACEcomplete, which is optimal for extensions of LTL. This result is shown using a novel linear size translation of RLTL expressions into 2way alternating parity automata on words. Unlike previous automatatheoretic approaches to LTL, this construction is compositional (bottomup). 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 ExpressionBased 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 Hoarestyle proof systems about programs with pointers, and there is an ongoing quest for understanding its complexity and expressive power. Herein, we show that firstorder separation logic with one record field restricted to two variables and ..."
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Separation logic is used as an assertion language for Hoarestyle proof systems about programs with pointers, and there is an ongoing quest for understanding its complexity and expressive power. Herein, we show that firstorder separation logic with one record field restricted to two variables and the separating implication (no separating conjunction) is as expressive as weak secondorder logic, substantially sharpening a previous result. Capturing weak secondorder logic with such a restricted form of separation logic requires substantial updates to known proof techniques. We develop these, and as a byproduct identify the smallest fragment of separation logic known to be undecidable: firstorder 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 Lineartime Temporal Logic
"... Abstract—This extended abstract presents the gist of regular lineartime temporal logic (RLTL), a logic that generalizes lineartime temporal logic (LTL) with the ability to use regular expressions arbitrarily as subexpressions. Unlike LTL, RLTL can define all ωregular languages and unlike previou ..."
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Abstract—This extended abstract presents the gist of regular lineartime temporal logic (RLTL), a logic that generalizes lineartime temporal logic (LTL) with the ability to use regular expressions arbitrarily as subexpressions. Unlike LTL, RLTL can define all ωregular languages and unlike previous approaches, RLTL is defined with an algebraic signature, does not depend on fixpoints in its syntax, and provides past operators via a single previousstep operator for basic state formulas. The satisfiability and model checking problems for RLTL are PSPACEcomplete, which is optimal for extensions of LTL. Keywordstemporal logic; LTL; regular expressions; I.