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Solving existentially quantified Horn clauses
 IN CAV
, 2013
"... Temporal verification of universal (i.e., valid for all computation paths) properties of various kinds of programs, e.g., procedural, multithreaded, or functional, can be reduced to finding solutions for equations in form of universally quantified Horn clauses extended with wellfoundedness condit ..."
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Temporal verification of universal (i.e., valid for all computation paths) properties of various kinds of programs, e.g., procedural, multithreaded, or functional, can be reduced to finding solutions for equations in form of universally quantified Horn clauses extended with wellfoundedness conditions. Dealing with existential properties (e.g., whether there exists a particular computation path), however, requires solving forallexists quantified Horn clauses, where the conclusion part of some clauses contains existentially quantified variables. For example, a deductive approach to CTL verification reduces to solving such clauses. In this paper we present a method for solving forallexists quantified Horn clauses extended with wellfoundedness conditions. Our method is based on a counterexampleguided abstraction refinement scheme to discover witnesses for existentially quantified variables. We also present an application of our solving method to automation of CTL verification of software, as well as its experimental evaluation.
Ranking function synthesis for bitvector relations
 In Proceedings of the 16th international conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS’10
, 2010
"... Abstract. Ranking function synthesis is a key aspect to the success of modern termination provers for imperative programs. While it is wellknown how to generate linear ranking functions for relations over (mathematical) integers or rationals, efficient synthesis of ranking functions for machinelev ..."
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Abstract. Ranking function synthesis is a key aspect to the success of modern termination provers for imperative programs. While it is wellknown how to generate linear ranking functions for relations over (mathematical) integers or rationals, efficient synthesis of ranking functions for machinelevel integers (bitvectors) is an open problem. This is particularly relevant for the verification of lowlevel code. We propose several novel algorithms to generate ranking functions for relations over machine integers: a complete method based on a reduction to Presburger arithmetic, and a templatematching approach for predefined classes of ranking functions based on reduction to SATand QBFsolving. The utility of our algorithms is demonstrated on examples drawn from Windows device drivers.
Solving qbf with counterexample guided refinement
 In SAT
, 2012
"... Abstract. We propose two novel approaches for using CounterexampleGuided Abstraction Refinement (CEGAR) in Quantified Boolean Formula (QBF) solvers. The first approach develops a recursive algorithm whose search is driven by CEGAR (rather than by DPLL). The second approach employs CEGAR as an addit ..."
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Cited by 21 (6 self)
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Abstract. We propose two novel approaches for using CounterexampleGuided Abstraction Refinement (CEGAR) in Quantified Boolean Formula (QBF) solvers. The first approach develops a recursive algorithm whose search is driven by CEGAR (rather than by DPLL). The second approach employs CEGAR as an additional learning technique in an existing DPLLbased QBF solver. Experimental evaluation of the implemented prototypes shows that the CEGARdriven solver outperforms existing solvers on a number of families in the QBFLIB and that the DPLL solver benefits from the additional type of learning. Thus this article opens two promising avenues in QBF: CEGARdriven solvers as an alternative to existing approaches and a novel type of learning in DPLL. 1
Abstractionbased algorithm for 2QBF
 In Proc. 14th International Conference on Theory and Applications of Satisfiability Testing (SAT 2011
, 2011
"... Abstract. Quantified Boolean Formulas (QBFs) enable standard representation of PSPACE problems. In particular, formulas with two quantifier levels (2QBFs) enable representing problems in the second level of the polynomial hierarchy (ΠP2, ΣP2). This paper proposes an algorithm for solving 2QBF satisf ..."
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Cited by 17 (5 self)
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Abstract. Quantified Boolean Formulas (QBFs) enable standard representation of PSPACE problems. In particular, formulas with two quantifier levels (2QBFs) enable representing problems in the second level of the polynomial hierarchy (ΠP2, ΣP2). This paper proposes an algorithm for solving 2QBF satisfiability by counterexample guided abstraction refinement (CEGAR). This represents an alternative approach to 2QBF satisfiability and, by extension, to solving decision problems in the second level of polynomial hierarchy. In addition, the paper presents a comparison of a prototype implementing the presented algorithm to state of the art QBF solvers, showing that a larger set of instances is solved. 1
ComplexitySensitive Decision Procedures for Abstract Argumentation
, 2012
"... Abstract argumentation frameworks (AFs) provide the basis for various reasoning problems in the areas of Knowledge Representation and Artificial Intelligence. Efficient evaluation of AFs has thus been identified as an important research challenge. So far, implemented systems for evaluating AFs have ..."
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Cited by 12 (6 self)
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Abstract argumentation frameworks (AFs) provide the basis for various reasoning problems in the areas of Knowledge Representation and Artificial Intelligence. Efficient evaluation of AFs has thus been identified as an important research challenge. So far, implemented systems for evaluating AFs have either followed a straightforward reductionbased approach or been limited to certain tractable classes of AFs. In this work, we present a generic approach for reasoning over AFs, based on the novel concept of complexitysensitivity. Establishing the theoretical foundations of this approach, we derive several new complexity results for preferred, semistable and stage semantics which complement the current complexity landscape for abstract argumentation, providing further understanding on the sources of intractability of AF reasoning problems. The introduced generic framework exploits decision procedures for problems of lower complexity whenever possible. This allows, in particular, instantiations of the generic framework via harnessing in an iterative way current sophisticated Boolean satisfiability (SAT) solver technology for solving the considered AF reasoning problems. First experimental results show that the SATbased instantiation of our novel approach outperforms existing systems.
A.: A DPLL algorithm for solving DQBF
 In: Proc. POS’12. (2012
"... Abstract. Dependency Quantified Boolean Formulas (DQBF) comprise the set of propositional formulas which can be formulated by adding Henkin quantifiers to Boolean logic. We are not aware of any published attempt in solving this class of formulas in practice. However with DQBF being NEXPTIMEcomplete ..."
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Abstract. Dependency Quantified Boolean Formulas (DQBF) comprise the set of propositional formulas which can be formulated by adding Henkin quantifiers to Boolean logic. We are not aware of any published attempt in solving this class of formulas in practice. However with DQBF being NEXPTIMEcomplete, efficient ways of solving it would have many practical applications. In this paper we describe a DPLLstyle approach (DQDPLL) for solving DQBF. We show how methods successfully applied in similar algorithms for SAT/QBF can be lifted to this richer logic. This enables to reuse efficient SAT and QBF solving techniques. 1
DataDriven Equivalence Checking
"... We present a data driven algorithm for equivalence checking of two loops. The algorithm infers simulation relations using data from test runs. Once a candidate simulation relation has been obtained, offtheshelf SMT solvers are used to check whether the simulation relation actually holds. The algor ..."
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Cited by 6 (3 self)
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We present a data driven algorithm for equivalence checking of two loops. The algorithm infers simulation relations using data from test runs. Once a candidate simulation relation has been obtained, offtheshelf SMT solvers are used to check whether the simulation relation actually holds. The algorithm is sound: insufficient data will cause the proof to fail. We demonstrate a prototype implementation, called DDEC, of our algorithm, which is the first sound equivalence checker for loops written in x86 assembly. 1.
SMTbased analysis of biological computation
 In NASA Formal Methods
, 2013
"... Abstract. Synthetic biology focuses on the reengineering of living organisms for useful purposes while DNA computing targets the construction of therapeutics and computational circuits directly from DNA strands. The complexity of biological systems is a major engineering challenge and their modeli ..."
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Abstract. Synthetic biology focuses on the reengineering of living organisms for useful purposes while DNA computing targets the construction of therapeutics and computational circuits directly from DNA strands. The complexity of biological systems is a major engineering challenge and their modeling relies on a number of diverse formalisms. Moreover, many applications are "missioncritical" (e.g. as recognized by NASA's Synthetic Biology Initiative) and require robustness which is difficult to obtain. The ability to formally specify desired behavior and perform automated computational analysis of system models can help address these challenges, but today there are no unifying scalable analysis frameworks capable of dealing with this complexity. In this work, we study pertinent problems and modeling formalisms for DNA computing and synthetic biology and describe how they can be formalized and encoded to allow analysis using Satisfiability Modulo Theories (SMT). This work highlights biological engineering as a domain that can benefit extensively from the application of formal methods. It provides a step towards the use of such methods in computational design frameworks for biology and is part of a more general effort towards the formalization of biology and the study of biological computation.
Termination Analysis of Imperative Programs Using Bitvector Arithmetic
, 2012
"... Currently, nearly all methods for proving termination of imperative programs apply an unsound and incomplete abstraction by treating bitvectors and bitvector arithmetic as (unbounded) integers and integer arithmetic, respectively. This abstraction ignores the wraparound behavior caused by under a ..."
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Cited by 4 (0 self)
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Currently, nearly all methods for proving termination of imperative programs apply an unsound and incomplete abstraction by treating bitvectors and bitvector arithmetic as (unbounded) integers and integer arithmetic, respectively. This abstraction ignores the wraparound behavior caused by under and overflows in bitvector arithmetic operations. This is particularly problematic in the termination analysis of lowlevel system code. This paper proposes a novel method for encoding the wraparound behavior of bitvector arithmetic within integer arithmetic. Afterwards, existing methods for reasoning about the termination of integer arithmetic programs can be employed for reasoning about the termination of bitvector arithmetic programs. An empirical evaluation shows the practicality and effectiveness of the proposed method.
More on the Complexity of QuantifierFree FixedSize BitVector Logics with Binary Encoding
"... Abstract. Bitprecise reasoning is important for many practical applications of Satisfiability Modulo Theories (SMT). In recent years, efficient approaches for solving fixedsize bitvector formulas have been developed. From the theoretical point of view, only few results on the complexity of fixed ..."
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Cited by 3 (1 self)
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Abstract. Bitprecise reasoning is important for many practical applications of Satisfiability Modulo Theories (SMT). In recent years, efficient approaches for solving fixedsize bitvector formulas have been developed. From the theoretical point of view, only few results on the complexity of fixedsize bitvector logics have been published. Most of these results only hold if unary encoding on the bitwidth of bitvectors is used. In previous work [1], we showed that binary encoding adds more expressiveness to bitvector logics, e.g. it makes fixedsize bitvector logic without uninterpreted functions nor quantification NExpTimecomplete. In this paper, we look at the quantifierfree case again and propose two new results. While it is enough to consider logics with bitwise operations, equality, and shift by constant to derive NExpTimecompleteness, we show that the logic becomes PSpacecomplete if, instead of shift by constant, only shift by 1 is permitted, and even NPcomplete if no shifts are allowed at all. 1