Zohar Manna

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Papers by Zohar Manna

Termination of polynomial programs

Verification, Model Checking, and Abstract …, 2005

We present a technique to prove termination of multipath polynomial programs, an expressive class... more

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The modal logic of programs

Lecture Notes in Computer Science, 1979

We explore the general framework of Modal Logic and its applicability to program reasoning. We re... more We explore the general framework of Modal Logic and its applicability to program reasoning. We relate the basic concepts of Modal Logic to the programming environment: the concept of &quot;world&quot; corresponds to a program state, and the concept of &quot;accessibility relation&quot; corresponds to the relation of derivability between states during execution. Thus we adopt the Temporal interpretation of Modal Logic.

Scalable Analysis of Linear Systems Using Mathematical Programming

Lecture Notes in Computer Science, 2005

We present a method for generating linear invariants for large systems. The method performs forwa... more We present a method for generating linear invariants for large systems. The method performs forward propagation in an abstract domain consisting of arbitrary polyhedra of a predefined fixed shape. The basic operations on the domain like abstraction, intersection, join and inclusion tests are all posed as linear optimization queries, which can be solved efficiently by existing LP solvers. The number and dimensionality of the LP queries are polynomial in the program dimensionality, size and the number of target invariants. The method generalizes similar analyses in the interval, octagon, and octahedra domains, without resorting to polyhedral manipulations. We demonstrate the performance of our method on some benchmark programs. ⋆

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Fixed Point Iteration for Computing the Time Elapse Operator

Lecture Notes in Computer Science, 2006

We investigate techniques for automatically generating symbolic approximations to the time soluti... more We investigate techniques for automatically generating symbolic approximations to the time solution of a system of differential equations. This is an important primitive operation for the safety analysis of continuous and hybrid systems. In this paper we design a time elapse operator that computes a symbolic over-approximation of time solutions to a continous system starting from a given inital region. Our approach is iterative over the cone of functions (drawn from a suitable universe) that are non negative over the initial region. At each stage, we iteratively remove functions from the cone whose Lie derivatives do not lie inside the current iterate. If the iteration converges, the set of states defined by the final iterate is shown to contain all the time successors of the initial region. The convergence of the iteration can be forced using abstract interpretation operations such as widening and narrowing. We instantiate our technique to linear hybrid systems with piecewiseaffine dynamics to compute polyhedral approximations to the time successors. Using our prototype implementation TimePass, we demonstrate the performance of our technique on benchmark examples.

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The logical basis for computer programming- volume 1: deductive reasoning

ABSTRACT

Synthesis: dreams &equil;> programs

The logical basis for computer programming

... The Logical Basis for Computer Programming. ... Publication: · Book, The Logical Basis for Co... more

Towards automatic program synthesis

Lecture Notes in Mathematics, 1971

Without Abstract

The special-relation rules are incomplete

Lecture Notes in Computer Science, 1992

The special-relation rules give accelerated treatment to transitivity, substitutivity, and other ... more The special-relation rules give accelerated treatment to transitivity, substitutivity, and other axioms classed as monotonicity properties. These rules extend paramodulation and other equality rules to relations other than equality. In this paper, it is established that these rules are all logically incomplete. The incompleteness of the negative paramodulation rule of Wos and McCune is also demonstrated.

A Decision Algorithm for Full Propositional Temporal Logic

Computer Aided Verification, 1993

The paper presents an efficient algorithm for checking the satisfiability of a propositional line... more The paper presents an efficient algorithm for checking the satisfiability of a propositional linear time temporal logic formula, which may have past as well as future operators. This algorithm can be used to check validity of such formulas over all models as well as over computations of a finite-state program (model checking). Unlike previous theoretical presentations of a decision method

Annotation-based deduction in temporal logic

Lecture Notes in Computer Science, 1994

This paper presents a deductive system for predicate temporal logic with induction. Representing ... more This paper presents a deductive system for predicate temporal logic with induction. Representing temporal operators by rst-order expressions enables temporal deduction to use the already developed techniques of rst-order deduction. But when translating from temporal logic to rst-order logic is done indiscriminately, the ensuing quanti cations and comparisons of time expressions encumber formulas, hindering deduction. So in the deductive system presented here, translation occurs more carefully, via rei cation rules. These rules paraphrase selected temporal formulas as nontemporal rst-order formulas with time annotations. This time reication process suppresses quanti cations (the process is analogous to quanti er skolemization) and uses addition instead of complicated combinations of comparisons. Some ordering conditions on arithmetic expressions can arise, but such are handled automatically by a specialpurpose uni cation algorithm plus a decision procedure for Presburger arithmetic. This deductive system is relatively complete.

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Verification of concurrent programs: a temporal proof system

ABSTRACT AMIR PNUELI Applied Mathematics,Department The Weizmann,Institute Rehovot, Israel This i... more

The temporal logic of reactive concurrent systems

The temporal logic o] reactive and concurrent systems

Reasoning in interval temporal logic

by Ben Moszkowski and Zohar Manna

Lecture Notes in Computer Science, 1984

Predicate logic is a powerful and general descriptive formalism with a long history of developmen... more Predicate logic is a powerful and general descriptive formalism with a long history of development. However, since the logic&#39;s underlying semantics have no notion of time, statements such as I increases by 2 cannot be directly expressed. We discuss interval temporal logic (ITL), a formalism that augments standard predicate logic with operators for time-dependent concepts. Our earlier work used ITL

A hardware semantics based on temporal intervals

by Zohar Manna and Ben Moszkowski

Lecture Notes in Computer Science, 1983

We present an interval-based temporal logic that permits the rigorous specification of a variety ... more We present an interval-based temporal logic that permits the rigorous specification of a variety of hardware components and facilitates proving properties such as correctness of implementation. Conceptual levels of circuit operation ranging from detailed quantitative timing and signal propagation up to functional behavior are integrated in a unified way.

A Family of Distributed Deadlock Avoidance Protocols and Their Reachable State Spaces

Lecture Notes in Computer Science, 2007

We study resource management in distributed systems. Incorrect handling of resources may lead to ... more We study resource management in distributed systems. Incorrect handling of resources may lead to deadlocks, missed deadlines, priority inversions, and other forms of incorrect behavior or degraded performance. While in centralized systems deadlock avoidance is commonly used to ensure correct and efficient resource allocation, distributed deadlock avoidance is harder, and general solutions are considered impractical due to the high communication overhead. However, solutions that use only operations on local data exist if some static information about the possible sequences of remote invocations is known. We present a family of efficient distributed deadlock avoidance algorithms that subsumes previously known solutions as special instances. Even though different protocols within the family allow different levels of concurrency and consequently fewer or more executions, we prove that they all have the same set of reachable states, expressed by a global invariant. This result enables: (1) a design principle: the use of different protocols at different sites does not compromise deadlock avoidance;

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Constraint-Based Linear-Relations Analysis

Lecture Notes in Computer Science, 2004

Linear-relations analysis of transition systems discovers linear invariant relationships among th... more Linear-relations analysis of transition systems discovers linear invariant relationships among the variables of the system. These relationships help establish important safety and liveness properties. Efficient techniques for the analysis of systems using polyhedra have been explored, leading to the development of successful tools like HyTech. However, existing techniques rely on the use of approximations such as widening and extrapolation in order to ensure termination. In an earlier paper, we demonstrated the use of Farkas Lemma to provide a translation from the linear-relations analysis problem into a system of constraints on the unknown coefficients of a candidate invariant. However, since the constraints in question are non-linear, a naive application of the method does not scale. In this paper, we show that by some efficient simplifications and approximations to the quantifier elimination procedure, not only does the method scale to higher dimensions, but also enjoys performance advantages for some larger examples.

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Efficient Strongly Relational Polyhedral Analysis

Lecture Notes in Computer Science, 2005

Polyhedral analysis infers invariant linear equalities and inequalities of imperative programs. H... more Polyhedral analysis infers invariant linear equalities and inequalities of imperative programs. However, the exponential complexity of polyhedral operations such as image computation and convex hull limits the applicability of polyhedral analysis. Weakly relational domains such as intervals and octagons address the scalability issue by considering polyhedra whose constraints are drawn from a restricted, user-specified class. On the other hand, these domains rely solely on candidate expressions provided by the user. Therefore, they often fail to produce strong invariants. We propose a polynomial time approach to strongly relational analysis. We provide efficient implementations of join and post condition operations, achieving a trade off between performance and accuracy. We have implemented a strongly relational polyhedral analyzer for a subset of the C language. Initial experimental results on benchmark examples are encouraging.

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Non-linear loop invariant generation using Gröbner bases

ACM SIGPLAN Notices, 2004

We present a new technique for the generation of non-linear (algebraic) invariants of a program. ... more We present a new technique for the generation of non-linear (algebraic) invariants of a program. Our technique uses the theory of ideals over polynomial rings to reduce the non-linear invariant generation problem to a numerical constraint solving problem. So far, the literature on invariant generation has been focussed on the construction of linear invariants for linear programs. Consequently, there has been little progress toward non-linear invariant generation. In this paper, we demonstrate a technique that encodes the conditions for a given template assertion being an invariant into a set of constraints, such that all the solutions to these constraints correspond to non-linear (algebraic) loop invariants of the program. We discuss some trade-offs between the completeness of the technique and the tractability of the constraint-solving problem generated. The application of the technique is demonstrated on a few examples.

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