Temporal Stream Logic modulo Theories

Multiway Decision Graph (MDG) is a canonical representation of a subset of many-sorted first-order logic. It generalizes the logic of equality with abstract types and uninterpreted function symbols. The area of Satisfiability (SAT) ha s been the subject of intensive research in recent years, with significant theoretical and practical contributions. From a practical perspective, a large number of very effective SAT solvers have recently been proposed, most of which based on improvements made to the original Davis-Putnam algorithm. Local search algorithms have allowed solving extremely large satisfiable instances of SAT. The combination between various verification methodologies will enhance the capabilities of each and overcome their limitations. In this paper, we introduce a model checking methodology for MDG based models using MDG tool and SAT solver. We use SAT solver searching for feasible paths of reachable states satisfying the property under certain encoding constraints. Finally, we provide a case study showing the correctness and the efficiency of our approach.

A specification formalism for reactive systems defines a class of Ω-languages. We call a specification formalism fully decidable if it is constructively closed under boolean operations and has a decidable satisfiability (nonemptiness) problem. There are two important, robust classes of Ω-languages that are definable by fully decidable formalisms. The Ω -reqular languages are definable by finite automata, or equivalcntly, by the Sequential Calculus. The counter-free Ω-regular languages are definable by temporal logic, or equivalcntly, by the first-order fragment of the Sequential Calculus. The gap between both classes can be closed by finite counting (using automata connectives), or equivalently, by projection (existential second-order quantification over letters).A specification formalism for real-time systems defines a class of timed Ω-langnages, whose letters have real-numbered time stamps. Two popular ways of specifying timing constraints rely on the use of clocks, and on the use of time bounds for temporal operators. However, temporal logics with clocks or time bounds have undecidable satisfiability problems, and finite automata with clocks (so-called timed automata) are not closed under complement. Therefore, two fully decidable restrictions of these formalisms have been proposed. In the first case, clocks are restricted to event clocks, which measure distances to immediately preceding or succeeding events only. In the second case, time bounds are restricted to nonsingular intervals, which cannot specify the exact punctuality of events. We show that the resulting classes of timed Ω-languages are robust, and we explain their relationship.First, we show that temporal logic with event clocks defines the same class of timed Ω-languages as temporal logic with nonsingular time bounds, and we identify a first-order monadic theory that also defines this class. Second, we show that if the ability of finite counting is added to these formalisms, we obtain the class of timed Ω-languages that are definable by finite automata with event clocks, or equivalently, by a restricted second-order extension of the monadic theory. Third, we show that if projection is added, we obtain the class of timed Ω-languages that are definable by timed automata, or equivalently, by a richer second-order extension of the monadic theory. These results identify three robust classes of timed Ω-languages, of which the third, while popular, is not definable by a, fully decidable formalism. By contrast, the first two classes are definable by fully decidable formalisms from temporal logic, from automata theory, and from monadic logic. Since the gap between these two classes can be closed by finite counting, we dub them the timed Ω-regular languages and the timed counter-free Ω-rcgular languages, respectively.

We consider the first-order theory whose language has as nonlogical symbols the constant symbols 0 and 1, the binary relation symbols = and This theory of integers under addition is commonly called the 'Presburger Arithmetic' and is known to be decidable for truth [Presburger (1929), Hilbert and Bernays (1968)]. We prove here that there exists a decision procedure for this theory, involving quantifier elimination, for which there is a superexponential upper bound on the size of formula produced when all variables have been eliminated.

Separation logic (SL) is a widely used formalism for verifying programs that manipulate dynamically allocated memory, relying on the separating conjunction $$\star $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mo>⋆</mml:mo> </mml:math> to combine disjoint heap structures. The standard approach in SL lacks the expressive power to handle overlaid data structures where multiple structures share some locations. We consider a logic that extends SL with a new separating conjunction operator "Image missing", enabling the composition of heaps with shared locations that allocate distinct fields. Our fragment supports generic inductive definitions and introduces set variables to constrain the locations shared by overlapping structures. We prove that the satisfiability problem for this fragment is in Nexptime , by reducing it to the satisfiability problem in BAPA [11], a decidable logic combining Boolean algebra of sets and Presburger arithmetic.

The logic of Counters, Lambdas, and Uninterpreted functions (CLU) is a subset of first-order logic satisfying the twin properties that 1) the validity of a CLU formula can be decided by generating a Boolean formula and using a Boolean satisfiability (SAT) checker to show the formula is unsatisfiable, and 2) it has sufficient expressive power to construct models of a variety of interesting software and hardware systems. We describe this logic and show its modeling capabilities.

Multiway decision graph (MDG) is a canonical representation of a subset of many-sorted first-order logic. It generalises the logic of equality with abstract types and uninterpreted function symbols. The area of satisfiability (SAT) has been the subject of intensive research in recent years, with significant theoretical and practical contributions. In this paper, we propose a new design verification tool integrating MDG and SAT, to check the safety of a design by invariant checking. Using MDG to encode the set of states provides a powerful mean of abstraction. We use a SAT solver to search for paths of reachable states violating the property under certain encoding constraints. In addition, we introduce an automated conversion-verification methodology to convert a directed formula (DF) into a conjunctive normal form (CNF) formula that can be fed to a SAT solver. The formal verification of this conversion is conducted within the HOL theorem prover. Finally, we present experimental results and a case study to show the correctness and the efficiency of our proposed methodology.

This paper focuses on the application of a real time tow monitoring system and the design of a hybrid shear plate and tubular tiedown system. The systems were used for the tow of a 700 foot jacket transported from South Korea to Offshore California. The objectives, design and use of the monitoring system are addressed. The impact of using a rigid barge assumption versus a flexible barge for tiedown design is presented along with the subsequent logic for choosing a hybrid design. INTRODUCTION In the past 10 years, the size and complexity of structures transported by sea have increased dramatically. With the world economic situation of today, voyages from the fabrication site to installation site are of lengths that were not previously considered, often taking 45–60 days (1,2). With the long period of exposure to weather conditions in the open sea, the integrity of the structure, both strength and cyclic, becomes a critical design consideration. Since the orientation and loadings are considerably different than the inplace conditions, transport can have a significant impact on the amount of steel required in the structure (2, 3). It is encumbant upon the owner to determine the relative impact of increased design and construction costs versus the risk of damage to the structure at sea. The economic considerations are not limited just to the increased construction costs, but also to the impact of financing of the project should the field development be delayed. In addressing the situation, some of the engineering questions that arise include:What weather conditions should be considered;How will the structure/vessel combination respond to the design conditions;How effective will transport personnel be in assessing conditions and taking corrective action, if any can be taken. AS the transit routes have lengthened, the industry has developed procedures to predict the behavior of the structures during transit. Recently, interest has been focused on large structures due to the 'flexible' nature of the launch barge (3,4). In using the procedures, several critical assumptions are required by the analyst/designer (5). Unfortunately, very limited data has been reported to qualify the accuracy of the assumptions (1,6) due to the few long tows undertaken and the cost and complexity of gathering reasonable data. With the development of field monitoring systems (6, 7), full scale tow monitoring projects are economical. A large scale tow monitoring project was undertaken for the trans-Pacific tow of the Harvest Jacket In an effort to lower the risk of damage by providing real-time jacket response data to the tug crew. A secondary objective was to obtain response data for post-voyage evaluation and correlation with design assumptions. This paper address the design of a hybrid tiedown system used to account for the flexibility of the launch barge and the development and use of a tow monitoring system.

We show that the satisfiability problem for LTL (with past operators) over arithmetic constraints (Constraint LTL) can be answered by solving a finite amount of instances of bounded satisfiability problems when atomic formulae belong to certain suitable fragments of Presburger arithmetic. A formula is boundedly satisfiable when it admits an ultimately periodic model of the form δπω, where δ and π are finite sequences of symbolic valuations. Therefore, for every formula there exists a completeness bound c, such that, if there is no ultimately periodic model with |δπ| ≤ c, then the formula is unsatisfiable.

Researchers have explored the application of combinatorial interaction testing (CIT) methods to construct samples to drive systematic testing of software system configurations. Applying CIT to highly-configurable software systems is complicated by the fact that, in many such systems, there are constraints between specific configuration parameters that render certain combinations invalid. Many CIT algorithms lack a mechanism to avoid these. In recent work, automated constraint solving methods have been combined with search-based CIT construction methods to address the constraint problem with promising results. However, these techniques can incur a non-trivial overhead. In this paper, we build upon our previous work to develop a family of greedy CIT sample generation algorithms that exploit calculations made by modern Boolean satisfiability (SAT) solvers to prune the search space of the CIT problem. We perform a comparative evaluation of the cost-effectiveness of these algorithms on four real-world highly-configurable software systems and on a population of synthetic examples that share the characteristics of those systems. In combination our techniques reduce the cost of CIT in the presence of constraints to 30 percent of the cost of widely-used unconstrained CIT methods without sacrificing the quality of the solutions.

Recently, Boolean Satisfiability (SAT) solving has been proposed to tackle the increasing complexity in high-level system design. Working well for system specifications with a limited amount of routing options, they tend to fail for densely connected computing platforms. This paper proposes an automated system design approach employing Answer Set Programming (ASP). ASP provides a stringent semantics, allowing for an efficient representation of routing options. An automotive case-study illustrates that the proposed ASP-based system design approach is competitive for sparsely connected computing platforms, while it outperforms SAT-based approaches for dense Networks-on-Chip by an order of magnitude.

Satisfiability Modulo Theories (SMT) is a decision problem for logical formulas over one or more first-order theories. In this paper, we study the problem of finding all solutions of an SMT problem with respect to a set of Boolean variables, henceforth All-SMT. First, we show how an All-SMT solver can benefit various domains of application: Bounded Model Checking, Automated Test Generation, Reliability analysis, and Quantitative Information Flow. Secondly, we then propose algorithms to design an All-SMT solver on top of an existing SMT solver, and implement it into a prototype tool, called aZ3. Thirdly, we create a set of benchmarks for All-SMT in the theory of linear integer arithmetic QF_LIA and the theory of bit vectors with arrays and uninterpreted functions QF_AUFBV. We compare aZ3 against Math SAT, the only existing All-SMT solver, on our benchmarks. Experimental results show that aZ3 is more precise than Math SAT.

This paper describes the integrated use of different knowledge types in an automated software engineering tool called REACH. These types include: (1) a first-order domain theory called the REA accounting model, (2) reconstructive expertise gleaned from textbooks on accounting system design in a bookkeeping environment, and (3) implementation compromise heuristics derived from the design experience of database designers. This tool aids an enterprise database analyst in the conceptual design stages of view modeling and view integration. Copyright © 1999 John Wiley & Sons, Ltd.

We describe the present status of the PEP-II asymmetric B factory design undertaken by SLAC, LBL, and LLNL. Design optimization and changes from the original CDR are described. R&D activities have focused primarily on the key technology areas of vacuum, RF, and feedback system design. Recent progress in these areas is described. The R&D results have verified our design assumptions and provide further confidence in the design of PEP-II. >

Beagle is an automated theorem prover for first-order logic modulo built-in theories. It implements a refined version of the hierarchic superposition calculus. This system description focuses on Beagle ’s proof procedure, background reasoning facilities, implementation, and experimental results.

One-counter processes are pushdown processes over a singleton stack alphabet (plus a stack-bottom symbol). We study the problems of model checking asynchronous products of one-counter processes against 1) first-order logic FO(R) with reachability predicate, 2) the finite variable fragments FO k(R) (k ≥ 2) of FO(R), 3) EF-logic which is a fragment of FO 2(R), and 4) all these logics extended with simple component-wise synchronizing predicates. We give a rather complete picture of their combined, expression, and data complexity. To this end, we show that these problems are poly-time reducible to two syntactic restrictions of Presburger Arithmetic, which are equi-expressive with first-order modulo counting theory of (ℕ, <), for which we give optimal quantifier elimination procedures. In particular, these problems are all shown to be in PSPACE, which is in sharp contrast to the closely related problem of model checking FO(R) over pushdown processes (with one stack) which has nonelementary complexity. Finally, we apply our proof method to give a fixed automatic (and so rational) graph whose modal logic theory has nonelementary complexity, solving a recently posed open question.KeywordsModel CheckLinear OrderAtomic FormulaMembership ProblemModel Check ProblemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.