Abstract: Techniques and systems for generating constrained random stimuli during functional verification of a design under verification (DUV) are described. Some embodiments can compute an observed probability distribution for each variable in a set of variables based on at least a first random solution generated using a set of constraints that are defined over the set of variables. The embodiments can then compute a correction probability distribution for each variable in the set of variables based on the observed probability distribution and an intended probability distribution. Next, while generating at least a second random solution using the set of constraints, the embodiments can select a random value for a given variable in the set of variables based on the correction probability distribution for the given variable. The observed probability distribution can be continuously updated and stored as constrained random stimuli are generated.

Abstract: A method for symbolic model checking for sequential systems using a combination of state-based and state-less approaches. A state-based method is used to compute frontier states by building transition relations on-the-fly using control flow information of the system, and performing successive image computations until a memory bound is reached, and efficiently storing only the new frontier states as disjunctive partitions of Boolean and Arithmetic expressions. A stateless method is used to check reachability of given goal states from a heuristically chosen set of frontier states until depth/time bound is reached. These two methods are alternated until one of the following occurs: all frontier states are explored, all goal states are reached, all computing resources are exhausted. Even though we do not store the entire reachable state set, we guarantee a complete coverage for terminating programs without the need to compute a fixed-point.

Abstract: A system and method for deciding the satisfiability of a non-linear real decision problem is disclosed. Linear and non-linear constraints associated with the problem are separated. The feasibility of the linear constraints is determined using a linear solver. The feasibility of the non-linear constraints is determined using a non-linear solver which employs interval constraint propagation. The interval solutions obtained from the non-linear solver are validated using the linear solver. If the solutions cannot be validated, linear constraints are learned to refine a search space associated with the problem. The learned constraints and the non-linear constraints are iteratively solved using the non-linear solver until either a feasible solution is obtained or no solution is possible.

Abstract: A system and method for solving a decision problem having Boolean combinations of linear and non-linear operations includes translating the non-linear real operations using a COordinate Rotation DIgital Computer (CORDIC) method programmed on a computer device into linear operations maintaining a given accuracy. Linear and translated linear operations are combined into a formula. Satisfiability of the formula is solved using a decision procedure for Boolean combinations of linear operations over integers and reals.

Abstract: Methods and systems for verifying the precision of a program that utilizes floating point operations are disclosed. Interval and affine arithmetic can be employed to build a model of the program including floating point operations and variables that are expressed as reals and integers, thereby permitting accurate determination of precision loss using a model checker. Abstract interpretation can be also employed to simplify the model. In addition, counterexample-guided abstraction refinement can be used to refine the values of parametric error constants introduced in the model.

Abstract: A system and method for determining satisfiability of a bounded model checking instance by restricting the decision variable ordering of the SAT solver to a sequence wherein a set of control state variables is given higher priority over the rest variables appearing in the formula. The order for control state variables is chosen based on an increasing order of the control path distance of corresponding control states from the target control state. The order of the control variables is fixed, while that of the rest is determined by the SAT search. Such a decision variable ordering strategy leads to improved performance of SAT solver by early detection and pruning of the infeasible path segments that are closer to target control state.

Abstract: Methods and systems for generating verification conditions and verifying the correctness of a concurrent system of program threads are described. The methods and systems determine and employ mutually atomic transactions to reduce verification problem sizes and state space for concurrent systems. The embodiments provide both an adequate and an optimal set of token-passing constraints for a bounded unrolling of threads.

Abstract: Systems and methods are disclosed for deciding a satisfiability problem with linear and non-linear operations by: encoding non-linear integer operations into encoded linear operations with Boolean constraints by Booleaning and linearizing, combining the linear and encoded linear operations into a formula, solving the satisifiability of the formula using a solver, wherein the encoding and solving includes at least one of following: a. Booleanizing one of the non-linear operands by bit-wise structural decomposition b. Linearizing a non-linear operator by selectively choosing one of the operands for Booleanization c. Solving using an incremental lazy bounding refinement (LBR) procedure without re-encoding formula, and verifying the linear and non-linear operations in a computer software.

Abstract: A system and method for determining satisfiability of a bounded model checking instance by restricting the decision variable ordering of the SAT solver to a sequence wherein a set of control state variables is given higher priority over the rest variables appearing in the formula. The order for control state variables is chosen based on an increasing order of the control path distance of corresponding control states from the target control state. The order of the control variables is fixed, while that of the rest is determined by the SAT search. Such a decision variable ordering strategy leads to improved performance of SAT solver by early detection and pruning of the infeasible path segments that are closer to target control state.

Abstract: A system and method for deciding the satisfiability of a non-linear real decision problem is disclosed. Linear and non-linear constraints associated with the problem are separated. The feasibility of the linear constraints is determined using a linear solver. The feasibility of the non-linear constraints is determined using a non-linear solver which employs interval constraint propagation. The interval solutions obtained from the non-linear solver are validated using the linear solver. If the solutions cannot be validated, linear constraints are learned to refine a search space associated with the problem. The learned constraints and the non-linear constraints are iteratively solved using the non-linear solver until either a feasible solution is obtained or no solution is possible.

Abstract: A system and method for bounded model checking of computer programs includes providing a program having at least one reachable property node. The program is decomposed for bounded model checking (BMC) into subproblems by creating a tunnel based on disjunctive control paths through the program. A reduced BMC sub-problem obtained using BMC unrolling, while using path constraints imposed by the at least one tunnel. For the reachable property node, determining a quantifier-free formula (QFP) in a decidable subset of first order logic. Satisfiability of the QFP is checked, independently and individually, to determine whether the QFP is satisfiable for the subproblem. The decomposing is continued until the a BMC bound is reached.

Abstract: A method for symbolic model checking for sequential systems using a combination of state-based and state-less approaches. A state-based method is used to compute frontier states by building transition relations on-the-fly using control flow information of the system, and performing successive image computations until a memory bound is reached, and efficiently storing only the new frontier states as disjunctive partitions of Boolean and Arithmetic expressions. A stateless method is used to check reachability of given goal states from a heuristically chosen set of frontier states until depth/time bound is reached. These two methods are alternated until one of the following occurs: all frontier states are explored, all goal states are reached, all computing resources are exhausted. Even though we do not store the entire reachable state set, we guarantee a complete coverage for terminating programs without the need to compute a fixed-point.

Abstract: Methods and systems for verifying the precision of a program that utilizes floating point operations are disclosed. Interval and affine arithmetic can be employed to build a model of the program including floating point operations and variables that are expressed as reals and integers, thereby permitting accurate determination of precision loss using a model checker. Abstract interpretation can be also employed to simplify the model. In addition, counterexample-guided abstraction refinement can be used to refine the values of parametric error constants introduced in the model.

Abstract: A system and method for solving a decision problem having Boolean combinations of linear and non-linear operations includes translating the non-linear real operations using a COordinate Rotation DIgital Computer (CORDIC) method programmed on a computer device into linear operations maintaining a given accuracy. Linear and translated linear operations are combined into a formula. Satisfiablity of the formula is solved using a decision procedure for Boolean combinations of linear operations over integers and reals.

Abstract: Methods and systems for generating verification conditions and verifying the correctness of a concurrent system of program threads are described. The methods and systems determine and employ mutually atomic transactions to reduce verification problem sizes and state space for concurrent systems. The embodiments provide both an adequate and an optimal set of token-passing constraints for a bounded unrolling of threads.

Abstract: Systems and methods are disclosed for performing error diagnosis of software errors in a program by from one or more error traces, building a repair program containing one or more modified program semantics corresponding to fixes to observed errors; encoding the repair program with constraints, biases and priortization into a constraint weighted problem; and solving the constraint weighted problem to generate one or more repair solutions, wherein the encoding includes at least one of: a) constraining one or more repairs choices guided by automatically inferring one or more partial specifications of intended program behaviors and program structure; b) biasing one or more repair choices guided by typical programming mistakes; and c) prioritizing the repair solutions based on error locations and possible changes in program semantics.

Abstract: Systems and methods are disclosed for deciding a satisfiability problem with linear and non-linear operations by: encoding non-linear integer operations into encoded linear operations with Boolean constraints by Booleaning and linearizing, combining the linear and encoded linear operations into a formula, solving the satisifiability of the formula using a solver, wherein the encoding and solving includes at least one of following: a. Booleanizing one of the non-linear operands by bit-wise structural decomposition b. Linearizing a non-linear operator by selectively choosing one of the operands for Booleanization c. Solving using an incremental lazy bounding refinement (LBR) procedure without re-encoding formula, and verifying the linear and non-linear operations in a computer software.

Abstract: A system and method for program testing includes, using a static analysis, determining dependency relations of enabled running processes in a program. The dependency relations are organized in a matrix to provide an interface for exploring the program. A reduced set of possible executions obtained by removal of redundant interleavings as determined with respect to the dependency relation, is explored on the program in a stateless exploration process that analyzes executed states and transitions to verify operation of the program.

Abstract: A system and method for bounded model checking of computer programs includes providing a program having at least one reachable property node. The program is decomposed for bounded model checking (BMC) into subproblems by creating a tunnel based on disjunctive control paths through the program. A reduced BMC sub-problem obtained using BMC unrolling, while using path constraints imposed by the at least one tunnel. For the reachable property node, determining a quantifier-free formula (QFP) in a decidable subset of first order logic. Satisfiability of the QFP is checked, independently and individually, to determine whether the QFP is satisfiable for the subproblem. The decomposing is continued until the a BMC bound is reached.

Abstract: An efficient approach for SAT-based quantifier elimination and pre-image computation using unrolled designs that significantly improves the performance of pre-image and fix-point computation in SAT-based unbounded symbolic model checking.