Florian Pigorsch

Siemens EDA

Craig interpolation has turned out to be an essential method for many applications in formal verification. In this paper we focus on the computation of simple interpolants for the theory of linear arithmetic with rational coefficients. We successfully minimize the number of linear constraints in the final interpolant by several methods including pr...

Craig interpolation has become a powerful and universal tool in the formal verification domain, where it is used not only for Boolean systems, but also for timed systems, hybrid systems, and software programs. The latter systems demand interpolation for fragments of first-order logic. When it comes to model checking, the structural compactness of i...

We propose an improved symbolic algorithm for the verification of linear hybrid automata with large discrete state spaces (where an explicit representation of discrete states is difficult). Here both the discrete part and the continuous part of the hybrid state space are represented by one symbolic representation called LinAIGs. LinAIGs represent (...

In this paper we present a novel QBF solving technique which is based on the integration of a search based (DPLL) and a rewriting based approach: While traversing the search space in a DPLL manner, we iteratively generate many sub-problems, which are handed over to the rewriting method one by one. Instead of just communicating back satisfiability r...

In this paper we introduce a new formal model, called finite state machines with time (FSMT), to represent real-time systems. We present a model checking algorithm for FSMTs, which works on fully symbolic state sets containing both the clock values and the state variables. In order to verify timed automata (TAs) with our model checking algorithm, w...

In this paper we present a method for integrating two complementary solving techniques for QBF formulas, i. e. variable elimination based on an AIG-framework and search with DPLL based solving. We develop a sophisticated mechanism for coupling these techniques, enabling the transfer of partial results from the variable elimination part to the searc...

In this paper we present a solver for Quantified Boolean Formulas (QBFs) which is based on And-Inverter Graphs (AIGs). We use a new quantifier elimination method for AIGs, which heuristically combines cofactor-based quantifier elimination with quantification using BDDs and thus benefits from the strengths of both data structures. Moreover, we prese...

In this paper we present a procedure for solving quantified boolean formulas (QBF), which uses And-Inverter Graphs (AIGs) as the core data-structure. We make extensive use of structural information extracted from the input formula such as functional definitions of variables and non-linear quan- tifier structures. We show how this information can di...

We present a method which computes optimized representations for non-convex polyhedra. Our method detects so-called redundant linear constraints in these representations by using an incremental SMT (Satisfiability Modulo Theories) solver and then removes the redundant constraints based on Craig interpolation. The approach is motivated by applicatio...

In this paper we present an approach to exploit pre-calculated implication knowledge in the construction of LinAIGs which represent sets of states of Linear Hybrid Systems. Our method computes implications between linear constraints and uses this information to strengthen SAT-based equivalence checks which occur during the construction of the LinAI...

We present a method which computes optimized representations for non-convex polyhedra. Our method detects so-called redundant linear constraints in these representations by using an incremental SMT solver and then removes the redundant constraints based on Craig interpolation. The approach is evaluated both for formulas from the model checking cont...

We propose algorithms significantly extending the limits for maintaining exact representations in the verification of linear hybrid systems with large discrete state spaces. We use AND-Inverter Graphs (AIGs) extended with linear constraints (LinAIGs) as symbolic representation of the hybrid state space, and show how methods for maintaining compactn...

Abstract—In this paper,we,present,a complete,method,for verifying properties expressed,in the temporal,logic CTL. In con- trast to the majority,of verification methods,presented,in recent years, we support unbounded model checking based on symbolic representations of characteristic functions. Among others, our method,is based,on an,advanced,And-Inv...

We address the problem of model checking hybrid systems which exhibit nontrivial discrete behavior and thus cannot be treated by considering the discrete states one by one, as most currently available verification tools do. Our procedure relies on a deep integration of several techniques and tools. An extension of AND-Inverter-Graphs (AIGs) with fi...

In this paper we present a complete method for verifying properties ex- pressed in the temporal logic CTL. In contrast to the majority of veriflca- tion methods presented in recent years, we support unbounded model checking based on symbolic representations of characteristic functions. Among others, our method is based on an advanced And-Inverter G...