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123
Programs with Lists are Counter Automata
 In CAV’06, LNCS
, 2006
"... Abstract. We address the verification problem of programs manipulating oneselector linked data structures. We propose a new automated approach for checking safety and termination for these programs. Our approach is based on using heap graphs where list segments without sharing are collapsed, and cou ..."
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Cited by 55 (7 self)
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Abstract. We address the verification problem of programs manipulating oneselector linked data structures. We propose a new automated approach for checking safety and termination for these programs. Our approach is based on using heap graphs where list segments without sharing are collapsed, and counters are used to keep track of the number of elements in these segments. This allows to apply automatic analysis techniques and tools for counter automata in order to verify list programs. We show the effectiveness of our approach, in particular by verifying automatically termination of some sorting programs. 1
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 36 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
Deciding QuantifierFree Presburger Formulas Using Finite Instantiation Based on Parameterized Solution Bounds
 In Proc. 19 th LICS. IEEE
, 2003
"... Given a formula # in quantifierfree Presburger arithmetic, it is well known that, if there is a satisfying solution to #, there is one whose size, measured in bits, is polynomially bounded in the size of #. In this paper, we consider a special class of quantifierfree Presburger formulas in which m ..."
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Cited by 35 (7 self)
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Given a formula # in quantifierfree Presburger arithmetic, it is well known that, if there is a satisfying solution to #, there is one whose size, measured in bits, is polynomially bounded in the size of #. In this paper, we consider a special class of quantifierfree Presburger formulas in which most linear constraints are separation (di#erencebound) constraints, and the nonseparation constraints are sparse. This class has been observed to commonly occur in software verification problems. We derive a new solution bound in terms of parameters characterizing the sparseness of linear constraints and the number of nonseparation constraints, in addition to traditional measures of formula size. In particular, the number of bits needed per integer variable is linear in the number of nonseparation constraints and logarithmic in the number and size of nonzero coe#cients in them, but is otherwise independent of the total number of linear constraints in the formula. The derived bound can be used in a decision procedure based on instantiating integer variables over a finite domain and translating the input quantifierfree Presburger formula to an equisatisfiable Boolean formula, which is then checked using a Boolean satisfiability solver. We present empirical evidence indicating that this method can greatly outperform other decision procedures.
Deciding Boolean Algebra with Presburger Arithmetic
 J. of Automated Reasoning
"... Abstract. We describe an algorithm for deciding the firstorder multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded ..."
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Cited by 31 (26 self)
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Abstract. We describe an algorithm for deciding the firstorder multisorted theory BAPA, which combines 1) Boolean algebras of sets of uninterpreted elements (BA) and 2) Presburger arithmetic operations (PA). BAPA can express the relationship between integer variables and cardinalities of unbounded finite sets, and supports arbitrary quantification over sets and integers. Our original motivation for BAPA is deciding verification conditions that arise in the static analysis of data structure consistency properties. Data structures often use an integer variable to keep track of the number of elements they store; an invariant of such a data structure is that the value of the integer variable is equal to the number of elements stored in the data structure. When the data structure content is represented by a set, the resulting constraints can be captured in BAPA. BAPA formulas with quantifier alternations arise when verifying programs with annotations containing quantifiers, or when proving simulation relation conditions for refinement and equivalence of program fragments. Furthermore, BAPA constraints can be used for proving the termination of programs that manipulate data structures, as well as
Fast computation by population protocols with a leader
 IN DISTRIBUTED COMPUTING: 20TH INTERNATIONAL SYMPOSIUM, DISC 2006
, 2006
"... Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard population protocol model—in which finitestate agents interact in pairs under the control of an adversary scheduler—where all pairs are equally likely to be chosen for ea ..."
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Cited by 30 (6 self)
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Fast algorithms are presented for performing computations in a probabilistic population model. This is a variant of the standard population protocol model—in which finitestate agents interact in pairs under the control of an adversary scheduler—where all pairs are equally likely to be chosen for each interaction. It is shown that when a unique leader agent is provided in the initial population, the population can simulate a virtual register machine in which standard arithmetic operations like comparison, addition, subtraction, multiplication, and division can be simulated in O(n log 4 n) interactions with high probability. Applications include a reduction of the cost of computing a semilinear predicate to O(n log 4 n) interactions from the previously bestknown bound of O(n 2 log n) interactions and simulation of a LOGSPACE Turing machine using the same O(n log 4 n) interactions per step. These bounds on interactions translate into O(log 4 n) time per step in a natural model in which each agent participates in an expected Θ(1) interactions per time unit. The central method is the extensive use of epidemics to propagate information from and to the leader, combined with an epidemicbased phase clock used to detect when these epidemics are likely to be complete.
The computational power of population protocols
 Distributed Computing
"... We consider the model of population protocols introduced by Angluin et al. [AAD + 04], in which anonymous finitestate agents stably compute a predicate of the multiset of their inputs via twoway interactions in the allpairs family of communication networks. We prove that all predicates stably com ..."
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Cited by 28 (4 self)
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We consider the model of population protocols introduced by Angluin et al. [AAD + 04], in which anonymous finitestate agents stably compute a predicate of the multiset of their inputs via twoway interactions in the allpairs family of communication networks. We prove that all predicates stably computable in this model (and certain generalizations of it) are semilinear, answering a central open question about the power of the model. Removing the assumption of twoway interaction, we also consider several variants of the model in which agents communicate by anonymous messagepassing where the recipient of each message is chosen by an adversary and the sender is not identified to the recipient. These oneway models are distinguished by whether messages are delivered immediately or after a delay, whether a sender can record that it has sent a message, and whether a recipient can queue incoming messages, refusing to accept new messages until it has had a chance to send out messages of its own. We characterize the classes of predicates stably computable in each of these oneway models using natural subclasses of the semilinear predicates. 1
Mixed RealInteger Linear Quantifier Elimination
, 1999
"... Consider the elementary theory T of the real numbers in the language L having 0, 1 as constants, addition and subtraction and integer part as operations, and equality, order and congruences modulo natural number constants as relations. We show that T admits an effective quantifier elimination proced ..."
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Cited by 26 (1 self)
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Consider the elementary theory T of the real numbers in the language L having 0, 1 as constants, addition and subtraction and integer part as operations, and equality, order and congruences modulo natural number constants as relations. We show that T admits an effective quantifier elimination procedure and is decidable. Moreover this procedure provides sample answers for existentially quantified variables. The procedure comprises as special cases linear elimination for the reals and for Presburger arithmetic. We provide closely matching upper and lower bounds for the complexity of the quantifier elimination and decision problem for T . Applications include a characterization of T definable subsets of the real line, and the modeling of parametric mixed integer linear optimization, of continuous phenomena with periodicity, and the simulation and analysis of hybrid control systems. We also consider the elementary theory of reals in variations of this language in view of quantifier elimination...